Pan American World Airways, Inc. (Pan Am) and Alert Management Systems, Inc. (Alert) (collectively Pan Am, defendants or appellants) appeal from final judgments entered on September 9, 1992 in the United States District Court for the Eastern District of New York (Platt, C.J.) in three eases arising out of the Pan Am Flight 103 terrorist bombing that occurred over Lockerbie, Scotland in December 1988. The trial was bifurcated into a liability phase, binding on all plaintiffs whose cases were consolidated in this multidistrict litigation, and a damages phase governing the cases of the three plaintiffs before us. The damages phase will also set the standards for damage awards in future cases resulting from this tragic disaster.1
Few Americans have forgotten the bombing of Flight 103 over Lockerbie, Scotland a few days before Christmas in 1988. There were 259 Americans aboard Pan Am’s plane from all walks of life. Among the passengers were business executives, entrepreneurs, airline employees, and college students — including 38 Syracuse University students returning home from study abroad. Although four years have passed since this tragedy occurred, it remains vivid in our national consciousness, standing as a reminder of our *811collective vulnerability to wanton terrorist acts.
The 13-week liability trial controlled all. the consolidated cases that had been filed against Pan Am throughout the United States by the passengers’ and the crews’ survivors and representatives. Trial began April 27, 1992. The jurors heard lengthy testimony from 58 witnesses, much of which was introduced by the over 180 depositions obtained during massive discovery taken worldwide. At its close, the jury rendered a special verdict finding defendants guilty of wilful misconduct that caused the explosion and the crash.
At the conclusion of the damages phase $9,225,000 was awarded to the Pagnucco family, $9,000,000 to the Bainbridge family, and $1,735,000 to the Porter family. Decedents Pagnucco and Bainbridge had been PepsiCo attorneys, decedent Porter an electrician and part-time musician. The damage awards included damages for loss of society and damages for loss of parental care to adult children. No award for survival damages— sought by plaintiffs — was made because the jury found the passengers had suffered no conscious pain and suffering before their deaths. Pan Am and Alert appeal challenging the finding of liability and the damage awards.
BACKGROUND
On December 21,1988 a bomb exploded on Pan Am Flight 103 causing it to crash over Lockerbie, Scotland. The 243 passengers and 16 crew members aboard the flight traveling from London to New York all perished. Numerous plaintiffs, including those in the cases before us, brought wrongful death actions against Pan Am and Alert, a Pan Am affiliate that provided security services in London and in Frankfurt, where Flight 103 originated. All those actions were consolidated for trial in the Eastern District of New York.
A single jury trial was conducted before Chief Judge Platt to try the liability issues common to the passenger cases. The parties agreed that the case was governed by the Warsaw Convention, formally named the Convention for the Unification of Certain Rules Relating to International Transportation by Air, done at Warsaw, Oct. 12, 1929, 49 Stat. 3000, T.S. No. 876, 137 L.N.T.S. 11, reprinted at 49 U.S.C. app. § 1502 note (1988) [hereinafter Warsaw Convention]. Although the Warsaw Convention generally limits a carrier’s liability for damages to $75,-000 per passenger, Article 25 permits recovery of unlimited compensatory damages provided the carrier’s “wilful misconduct” caused the damages. An earlier decision of this Circuit established that punitive damages may not be collected under the Warsaw Convention. In Re Air Disaster at Lockerbie, Scotland on December 21, 1988 (“Lockerbie I”), 928 F.2d 1267 (2d Cir.), cert. denied, — U.S. -, 112 S.Ct. 331, 116 L.Ed.2d 272 (1991).
On July 10, 1992 the jury found that the defendants engaged in wilful misconduct that led to this fatal crash. The trial’s liability phase centered on Pan Am’s alleged noncompliance with Federal Aviation Administration (FAA) directives concerning baggage inspection, particularly with regard to unaccompanied baggage that might contain explosives. Additional proof was introduced regarding other alleged misconduct on the air carrier’s part. Plaintiffs contended that the bomb entered the flight on an unaccompanied bag that Pan Am, through its wilful misconduct, failed to inspect and detect. Under plaintiffs’ theory — detailed by several expert witnesses — the bomb was hidden inside a radio-cassette player packed in a bronze Samsonite suitcase. The suitcase supposedly traveled from Malta to Frankfurt on Air Malta Flight 180. There, the experts posited, it was transferred to the first leg of Flight 103 from Frankfurt to London, where it was then placed on Flight 103 bound for New York.
Although bags transferred from other flights to Flight 103 in Frankfurt were x-rayed, plaintiffs asserted the airline’s x-ray procedure violated security requirements contained in an FAA regulation at issue in this case, Air Carrier Standard Security Program or ACSSP XV.C.l.(a), which ensured that bags matched passengers and that any unaccompanied bags be physically inspected. Pan Am unsuccessfully argued to the jury *812that its actions did not amount to wilful misconduct, and that it was impossible to determine how the bomb was planted on Flight 108. To meet plaintiffs’ claims of wilful misconduct, Pan Am and Alert emphasized that the transferred bags had been examined using x-ray equipment, but that no bomb was discovered. They challenged plaintiffs’ theory of causation and suggested that even if there were any misconduct on their part, it did not lead to the crash.
In finding defendants liable the jury rendered a special verdict. On the special verdict form, it indicated that it had specifically found 1) that “Pan Am (including Alert) engage[d] in wilful misconduct,” and 2) that the wilful misconduct was “a substantial factor in causing the disaster.” Following the liability phase, the jury then awarded compensatory damages in the three plaintiffs’ cases. There are 207 other passenger cases pending, all awaiting the outcome of this appeal.
DISCUSSION
On appeal Pan Am rolls out a panoply of arguments, most involving evidence the district court excluded, and which, therefore, was not heard or considered by the jury. These contentions concern four broad areas: I) the exclusion of evidence related to Pan Am and Alert’s alleged noncompliance with ACSSP regulations concerning, unaccompanied baggage; II) the admission of evidence showing other alleged misconduct on appellants’ part coupled with the disallowance of defense testimony concerning alternate theories of causation; III) various other eviden-tiary rulings; and TV) the legal bases for the damage awards. In the discussion that follows, we examine each of these four areas in order.
I EXCLUDED EVIDENCE PAN AM AND ALERT ARGUE WOULD HAVE NEGATED ANY WILFUL MISCONDUCT ARISING FROM THEIR NONCOMPLIANCE WITH CERTAIN ACSSP REGULATIONS
Appellants insist the trial court committed reversible error in excluding several pieces of evidence that might have negated a finding of wilful misconduct based on appellants’ alleged failure to comply with FAA regulations concerning unaccompanied baggage. This first challenge centers on rulings excluding three lines of evidence that appellants believe were relevant to Pan Am and Alert’s state of mind, that is, their wilfulness. The main line of barred evidence purportedly demonstrated an oral waiver by the FAA, excusing Pan Am’s compliance with relevant security regulations. The breach of those regulations was central to plaintiffs’ case and, as a response, Pan Am and Alert sought to demonstrate that they thought they were complying with the FAA requirements.
The second piece of barred evidence was British regulations that did not require the observance of the same safety standards as did those of the FAA. Appellants sought to negate any inference of wilfulness on their part by showing that x-raying baggage transferred from other airlines—the procedure Pan Am followed—complied with the British regulations. The third piece of evidence not entertained was proof that some experts believe the highest threat to airline safety is not posed by unaccompanied baggage. Each of these three lines of evidence, appellants urge, might have negated plaintiffs’ showing of wilful misconduct.
The standard of liability under the Warsaw Convention, as already noted, requires that a carrier have engaged in “wilful misconduct” causing the claimed losses in order for plaintiffs to hold a carrier hable in an amount exceeding the Convention’s $75,-000 damage limit. See Warsaw Convention, art. 25. Wilful misconduct under the Convention means that a carrier must have acted either 1) with knowledge that its actions would probably result in injury or death, or 2) in conscious or reckless disregard of the fact that death or injury would be the probable consequence of its actions. See Ospina v. Trans World Airlines, Inc., 975 F.2d 35, 37 (2d Cir.1992), cert. denied, - U.S. -, 113 S.Ct. 1944, 123 L.Ed.2d 650 (1993); In re Korean Air Lines Disaster of September 1, 1983, 932 F.2d 1475, 1479 (D.C.Cir.), cert. denied, - U.S. -, 112 S.Ct. 616, 116 L.Ed.2d 638 (1991). The district court charged the jury under that standard and *813also charged it that the standard applied whether wilful misconduct resulted from an act or failure to act by the carrier. Appellants do not challenge the district court’s jury instruction as to wilful misconduct. Instead, they focus on the just recited three different lines of proof they were not allowed to present to guide the jury’s application of that standard, that is, the oral waiver, tbe British regulations, and expert testimony regarding the threat posed by unaccompanied baggage.
A. The Alleged Oral Waiver
We begin discussion by reference to the standard of review on appeal from an exclusion of evidence at trial. That standard establishes that the relevance and admissibility of proffered evidence rests in the sound discretion of the trial court. See, e.g., United States v. Corning, 968 F.2d 232, 238 (2d Cir.), cert. denied, -U.S. -, 113 S.Ct. 416, 121 L.Ed.2d 339 (1992); United States v. Ebner, 782 F.2d 1120, 1126 (2d Cir.1986). Defendants maintain that an FAA official granted them an oral waiver excusing strict compliance with certain FAA regulations, and that Chief Judge Platt abused his discretion when he disallowed their evidence purporting to demonstrate their belief in this waiver. Although Pan Am is imprecise as to the date of the purported waiver, it asserts it was given verbally to a Pan Am official. Virtually no written documentation supports it. Defendants’ argument essentially is that this evidence would have shown that their x-ray inspection of interline bags complied with FAA requirements or that, regardless of FAA requirements, they did not act with conscious or reckless disregard of the probable consequences of their x-ray procedures since they thought the safety precautions they were following were permissible.
1. The Unambiguous Nature of ACSSP Regulation XV C.l.(a)
In support of this point, Pan Am points out that a regulation may be interpreted orally, and that the regulation at issue is ambiguous and therefore susceptible to such an interpretation. We are unable to accept appellants’ premise that the supposed oral waiver was in fact an interpretation of an ambiguous regulation. As a matter of law the FAA regulation at issue here—ACSSP XV C.l.(a)—is not ambiguous, as the following discussion demonstrates.
In April 1986 the FAA established specific ACSSP regulations and mandated that they be followed at heightened security airports designated “extraordinary security”' airports. Both Frankfurt and London’s Heathrow airports were classified as “extraordinary security” airports. The central regulation at issue in this case, ACSSP regulation XV C.l.(a), concerns the detection of unaccompanied bags. It directs an air carrier operating out of an extraordinary security airport to
[cjonduct a positive passenger/checked baggage match resulting in physical, inspection or noncarriage of all unaccompanied bags. The carrier may use either physical match or administrative match, but, in either case, it should be done in a way that passengers are aware of the use of the procedures.
Air carriers like Pan Am, thus were required under the regulations first to do a physical or an administrative match to detect unaccompanied bags, and then to physically inspect any unaccompanied bags before they could be loaded. ACSSP XV C clearly ordered that an air carrier operating out of an extraordinary security airport “shall adopt and carry out the ... special procedures except where local conditions preclude and alternative measures have been approved by the FAA.”
Under ACSSP XV C.l.(a) the positive match is designed to ensure that any unaccompanied bags definitely will be identified as such. The regulation permits the positive match to be done either as a “physical match,” in which passengers identify their bags on the tarmac, or an “administrative match,” in which the number of passengers boarding the aircraft and the number of bags checked are compared with the number of bags to be loaded.
Pan Am claimed that it conducted an administrative match. Plaintiffs averred that this administrative match did not comply with the regulations because it was incomplete and failed to identify all unaccompanied *814bags. Particularly, plaintiffs point out Pan Am’s procedures did not identify the bags of interline passengers, i.e., those passengers who had transferred to a Pan Am flight from another airline and whose bags had been checked with the other airline at the passengers’ point of origin.
If a match conducted under the regulations revealed unaccompanied bags, the regulations expressly directed the airline to conduct the second step of the process, “physical inspection,” before it could carry the bags. ACSSP XV C.l.(a). Plaintiffs demonstrated that Pan Am and Alert. x-rayed all bags transferred from other carriers — so-called “interline” bags — but conducted no other inspection of such bags. Pan Am and Alert assert that physical inspection could be interpreted to mean an x-ray inspection. For several reasons, we think this a strained reading of the unambiguous regulation.
First, the FAA promulgated “Physical Inspection Guidelines” in the ACSSP which specified that physical inspection involves opening and inspecting all compartments of baggage. The guidelines do not mention x-ray as an acceptable means of inspection. Second, the jury heard testimony from Pan Am’s own General Manager at Heathrow, and other witnesses as well, that physical inspection under the regulations involved opening up bags and that x-raying them did not satisfy the regulation. Third, ACSSP regulations applicable at other, lower security airports explicitly permitted x-ray or physical inspections. Thus, it is plain that the regulations applicable at Frankfurt and London’s Heathrow were unambiguous: they did not permit x-ray inspections as a substitute for a physical inspection. Appellants’ reliance on United States v. Eastern Air Lines, Inc., 792 F.2d 1560, 1563 (11th Cir.1986), is inapposite because that ease involved a more broadly worded regulation, one susceptible to different interpretations.
We hold, therefore, that the district court did not err in refusing to allow witnesses — like the co-chair of the Pan Am Security Task Force, Richard Cozzi — to testify that they thought the regulations , were ambiguous. As a matter of law, ACSSP XV C.l.(a) is not ambiguous in requiring a positive match and physical inspection of unaccompanied bags before they may be carried on board a departing plane. Introducing testimony to the contrary would have invaded the court’s function of determining the law and instructing the jury as to that law. See FAA v. Landy, 705 F.2d 624, 632 (2d Cir.), cert. denied, 464 U.S. 895, 104 S.Ct. 243, 78 L.Ed.2d 232 (1983).
2. Proof of the Alleged Oral Waiver
Given that the FAA regulation in question is not ambiguous, Pan Am next asserts it obtained an oral waiver of the regulation from the FAA and that the district court erred in disallowing evidence of that waiver. Evidence showed that as of April 1986 Pan Am established procedures to ensure that unaccompanied interline bags were not carried on its airlines. However, the process for identifying unaccompanied interline bags proved too “cumbersome” and expensive. Pan Am therefore stopped performing a match for interline bags in London in February 1987 and in Frankfurt in July 1988. It also eliminated physical searches of unaccompanied interline bags. Thereafter bags were simply x-rayéd and put on board, rather than matched against particular tickets. This was a violation of ACSSP XIV, which requires Pan Am to advise the FAA in writing if interline bag match has been discontinued.
It is apparent therefore from the record that Pan Am made no distinction on Flight 103 between interline accompanied versus interline unaccompanied bags. Most significantly, the Flight 103 pilot was not informed about the presence of unaccompanied interline bags, in violation of ACSSP XIII E. Pan Am managers allegedly instructed gate employees in London not to advise pilots of unaccompanied bags because it made crews “jittery.”
What remains central to appellants’ defense is their reliance on x-ray alone to inspect interline bags transferred to Flight 103. They sought to introduce evidence that at 1986 and 1987 meetings, mostly with unidentified FAA officials, oral permission was purportedly given to Pan Am to allow it to *815deviate from the ACSSP regulations. Because of that waiver, they contend, they were in compliance with FAA requirements. They thus sought to show that their noncomplianee from the letter of the regulations was excused by an exemption.
Yet, the relevant regulations expressly require a written application for a waiver and written FAA approval based on certain findings. See 14 C.F.R. §§ 11.25, 11.27(e), 108.7(a)(2), 108.25(b)-(c) (1993); see also 49 U.S.C.App. §§ 1357(a)(2)(B), 1421(a)(6) & (c). The Director of the Office of Civil Aviation Security at the FAA at the time of the Pan Am bombing, Raymond Salazar, testified that in order to obtain an exemption from an ACSSP regulation an air carrier would have to file a written request and follow a specific procedure that was then in place. Salazar further denied ever granting an oral waiver to any Pan Am official or for that matter to any other air carrier. His predecessor at the FAA, Billie Vincent, testified to the same effect that written authorization and approval were required for exemption from ACSSP requirements.
Salazar was asked by plaintiffs to testify whether he had ever granted an oral waiver to a Pan Am official. The purpose of the question was to get an explanation of a statement contained in a Pan Am electronic mail (e-mail) memorandum. Plaintiffs produced the e-mail message that Pan Am security officer Daniel Sonesen had sent to the regional Pan Am security representatives at Heathrow and Frankfurt. The e-mail message, dated March 28, 1988, stated in part, “the Dir. FAA R Salizar has granted x ray as and [sic] alternative to searching pass, baggage.” Salazar testified that that representation was inaccurate and a misrepresentation, and when pressed by counsel, characterized it as “a falsehood.”
Despite requirements that exemptions be in writing, Pan Am offered no proof that it had ever applied for a written exemption from the provisions of ACSSP XV C.l.(a) at Heathrow or Frankfurt. There was evidence that Pan Am had made written applications on other occasions for exemptions from ACSSP XV C.l, 2, and 3, indicating that Pan Am was aware of the proper procedure for requesting a waiver. Further, Pan Am’s Chairman, Thomas Plaskett, admitted the airline knew waivers had to be in writing.
Although the FAA regulations occupied a key role in the trial of this case, it must be kept in mind that Pan Am and Alert’s compliance with them is not dispositive of the outcome. As appellants acknowledge in their brief, and as the' court instructed the jury, proof of full compliance with the ACSSP would not necessarily provide appellants with a complete defense against a claim of wilful misconduct. FAA regulations only establish minimum requirements for air carriers. A jury could conceivably find certain circumstances under which an air carrier had committed wilful misconduct even though it followed FAA regulations to the letter. Similarly, noncomplianee with ACSSP procedures will not necessarily lead to a per se finding of wilful misconduct. A carrier might not have acted with wilful misconduct, even were it to have failed to comply with an FAA regulation. The issue we are called upon to decide, thus, is whether evidence of Pan Am’s alleged oral waiver should have been admitted by the trial court.
(a) Proposed Testimony
The excluded evidence concerning the oral waiver primarily involved the testimony of three witnesses. We are told that the first witness, Daniel Sonesen, would have testified that he approached the FAA in 1986 and received a verbal authorization for the x-ray-only inspection of interline bags, though he could not recall who gave this authorization. He would have testified further, so defendants state, that at an October 1987 meeting with Salazar and others he was advised that x-ray inspection would comply with ACSSP requirements. Sonesen’s pretrial deposition testimony was before the district court, but we are unable to find in the record an express offer of proof of- what his testimony would have been. Moreover, our faith in the defendants’ versions of Sonesen’s testimony is not enhanced by the fact that Sonesen’s 1990 deposition testimony is substantially inconsistent with the representations made by the defendants before us. Simply put, the defendants refused to put Sonesen on the *816stand for their own reasons, and yet want us to accept at face value representations not made under oath, not subject to cross-examination, and in fact inconsistent with prior testimony made under oath. See, e.g., Fortunato v. Ford Motor Co., 464 F.2d 962, 967 (2d Cir.), cert. denied, 409 U.S. 1038, 93 S.Ct. 517, 34 L.Ed.2d 487 (1972) (stating that appellate court will not “permit a party to allege on appeal what it failed to claim to the trial court,” since that “would allow a party to obtain a new trial simply on its claim that it would have proven a certain fact or facts had it been given a chance”); Moss v. Hornig, 314 F.2d 89, 93 (2d Cir.1963) (holding that an appellate court cannot be expected to reverse where there was no offer of proof, and “where the significance of the evidence sought to be introduced is not obvious”);. Marrone v. United States, 355 F.2d 238, 241 (2d Cir.1966) (holding that the failure to make an offer of proof to demonstrate the significance of excluded testimony “must be held to be fatal,” even where persuasive authority indicated that the district court should have allowed the testimony).
The second witness proffered by the defense was the former co-chair of the Pan Am Security Task Force, Richard Cozzi. Although Cozzi testified at trial, he was not permitted to testify as to Pan Am’s purported verbal authorization from the FAA. Since his proposed testimony was preserved, we can see he would have testified that the Task Force in late 1986 wanted to find out if x-ray of interline bags would comply with the ACSSP, even though some members were doubtful it could comply; the Task Force instructed Sonesen to cheek with the FAA as to whether inspection by x-ray satisfied the ACSSP; and Sonesen reported back that he had done so and that the FAA said that x-ray inspection of interline bags would comply with the requirements. Even had Cozzi been permitted to testify on this issue, his statement respecting what Sonesen reported would have been inadmissible hearsay because it was offered for the truth of the matter asserted, to wit, that Salazar granted Pan Am a waiver of compliance with ACSSP XV C.l.(a). That Pan Am offered Cozzi’s testimony for this purpose is clear from the record:
.MR. Shaughnessy: You talked about what Mr. Sonesen told you about his discussions with the FAA. Do you have an opinion as to whether Mr. Sonesen was telling the truth?
Mr. Cozzi: Yes. I certainly believed Mr. Sonesen was telling the truth. There was no reason for him not to.
The third witness was Pan Am’s Chairman, Thomas Plaskett. Pan Am offered his testimony in an offer of proof, in which Plaskett stated that he did not recall having any conversations or information concerning whether the FAA had authorized Pan Am to use x-ray machines to examine luggage.
Additional evidence appellants sought, but were not allowed to introduce to show the supposed appropriateness of their procedures included testimony concerning a September 1988 FAA inspection at Heathrow at which Pan Am was not cited for violating ACSSP XV C.l.(a).
(b) Trial Court’s Rulings
In a series of oral rulings repeated throughout the record, the trial judge stated that any testimony by defense witnesses as to the purported verbal authorization would be excluded. It treated the proffered evidence as an attempt to mount a so-called government authorization defense, the bounds of which will be discussed shortly. Chief Judge Platt believed that a government authorization defense may only be predicated on authorization from a government official with power to grant such authorization. He held the defense unavailable because anyone who might have given a verbal exemption at the FAA would have had no authority to do so. The trial court also observed that any evidence as to a verbal authorization would be irrelevant since Pan Am was charged with knowing the regulations, including those that stated amendments and exemptions to the regulations must be in writing.
Before analyzing the government authorization defense, we briefly discuss one of defendants’ arguments for permitting the introduction of the verbal authorization de*817fense: to rebut Salazar’s statements concerning Sonesen’s e-mail message, which plaintiffs had introduced into evidence. A trial court may in the interests of fairness allow otherwise inadmissible evidence on an issue when necessary to rebut a false impression left by inadmissible evidence introduced by an opposing party. See, e.g., United States v. Rea, 958 F.2d 1206, 1225 (2d Cir.1992). But whether to entertain such sort of proof is left squarely in the trial judge’s discretion since the presider at trial is in a better position to assess how to conduct it- fairly than is an appellate court reading the record.
Here the district court did not abuse its discretion in declining to admit the evidence for this purpose. It directly offered Pan Am and Alert a curative instruction, stating, “[o]n the so-called verbal authorization, ... [i]f they want me to give the jury an instruction to disregard the testimony that came in at the outset of the case before I understood what the issue was, I will be glad to give that instruction.” Since appellants refused to ask for that instruction, they waived any complaint as to harm they may have suffered due to Salazar’s characterization of Sonesen’s e-mail as inaccurate. See United States v. Grubczak, 793 F.2d 458, 461-62 (2d Cir.1986).
Nor is there merit in Pan Am’s contention that it was an abuse of discretion to exclude testimony regarding a September 1988 FAA inspection at which Pan Am was not cited for violations relating to its x-ray procedure. Other evidence that was before the jury showed FAA inspections of Pan Am operations at Heathrow and Frankfurt had not resulted in any FAA citations.
Now turning to the substantive question of whether the district court erred in refusing to allow any evidence regarding the oral waiver, the plaintiffs’ argue initially that Pan .Am failed to make a proper offer of proof with respect to the evidence they sought to introduce. Assuming without deciding that defendants sufficiently preserved their objection does not change the result, as we demonstrate below.
We note that the parties and the district court frame the legal issue they faced in different ways. Chief Judge Platt thought-the offer of proof was an attempt by defendants to mount a government authorization defense. We believe the proffered proof also can be viewed as an attempt by defendants to invoke what is often referred to as a “mistake of law” defense. Defendants assert it was proof probative of defendants’ states of mind.
(i) Government Authorization
Chief Judge Platt correctly ruled that a government authorization defense was not available to Pan Am and Alert. Such defense requires a demonstration of “legitimate reliance on an official interpretation of law.” See United States v. Durrani, 835 F.2d 410, 422-23 (2d Cir.1987). Under orn-ease law, the official on whose interpretation the defendant allegedly relied must have actual authority. See United States v. Duggan, 743 F.2d 59, 83-84 (2d Cir.1984) (mistaken belief that individual had apparent government authority did not warrant submission of defense to jury); see also United States v. Schwartz, 924 F.2d 410, 422 (2d Cir.1991).
Here all the evidence demonstrated that amendments to or exemptions from ACSSP XV C.l.(a) had to be made in writing by the FAA following written application. Both Salazar and Vincent testified that as Directors of the FAA Office of Civil Aviation Security they did not have the authority to alter the ACSSP orally. The regulations support this view, as did testimony of Pan Am’s own witnesses. Pan Am’s attempted government authorization defense was therefore properly preeludéd by the district court because the FAA officials allegedly contacted simply did not have the actual authority to grant any verbal authorization for Pan Am’s x-ray-only inspection of interline bags.
(ii) Mistake of Law
Viewed as a mistake of law defense, defendants offered-the oral waiver evidence to show they thought what they were doing was in accordance with the law and, even if they were mistaken, under such a circumstance they should not be held liable for wilful misconduct. Yet, contrary to appellant’s view, even were a mistake of law *818defense one. that could be successfully interposed, it would not necessarily absolve Pan Am of liability in this Warsaw Convention case. The same standards governing the availability of .mistake of law govern even when it might not supply a complete defense to liability — in this case, for example, the jury might have found that complying with the FAA minimum requirements was still inadequate under the circumstances on the ultimate issue of wilful misconduct. The usual standards defining the permissibility of a mistake of law defense are as effective where the mistaken law is a regulation. See United States v. International Minerals & Chem. Corp., 402 U.S. 558, 563, 91 S.Ct. 1697, 1700-1701, 29 L.Ed.2d 178 (1971) (noting “principle that ignorance of the law is no defense applies whether the law be a statute or a duly promulgated and published regulation”).
In any event, the oral waiver evidence was inadmissible for purposes of showing that Pan Am’s violation of the FAA regulation was the result of a mistake of law. It has long been a maxim that “ignorance of the law is no excuse.” The reason for this ancient rule is not because everyone knows the law, but because ignorance of it is a ready excuse easily raised and difficult to refute. We and the Supreme Court regularly acknowledge that a mistaken view of the law usually will not serve as an acceptable defense. Durrani, 835 F.2d at 422; Cheek v. United States, 498 U.S. 192, 199, 111 S.Ct. 604, 609, 112 L.Ed.2d 617 (1991). While cases where the rule is cited typically involve criminal offenses, see, e.g., Cheek, 498 U.S. at 199, 111 S.Ct. at 609, it applies equally in civil cases. See Barlow v. United States, 32 U.S. (7 Pet.) 404, 411, 8 L.Ed. 728 (1833) (Story, J.) (“It is a common maxim, familiar to all minds, that ignorance of the law will not excuse any person, either civilly or criminally-”); Ruley v. Nelson, 106 F.R.D. 514, 518 (D.Nev.1985) (noting ignorance of law is no excuse.in civil or criminal law).
In Cheek v. United States, 498 U.S. 192, 111 S.Ct. 604, 112 L.Ed.2d 617 (1991), now a seminal case in the area, the Supreme Court declared that the term “wilfully” in federal criminal tax statutes carved out an exception to the general maxim that ignorance of the law is no excuse. Id. at 199-200, 111 S.Ct. at 609-610. The Court said that the wilfulness requirement in the tax laws required the defendant to be allowed to introduce evidence as to any belief — no matter how objectively unreasonable that belief might be— tending to show an unawareness of a legal duty on defendant’s part. Id. at 203, 111 S.Ct. at 611.
In doing so, the Supreme Court carefully limited its decision to the tax field. It emphasized “the complexity” of the tax laws, 498 U.S. at 200, 111 S.Ct. at 609, the difficulty of the “average citizen” in comprehending duties imposed by the tax laws, id. at 199, 111 S.Ct. at 609, and constructions of the term “wilfulness” in the tax context, id. at 201, 111 S.Ct. at 610. Our subsequent decisions and those of other courts acknowledge Cheek’s limited application. See, e.g., United States v. Caming, 968 F.2d 232, 240 (2d Cir.) (collecting other circuits’ cases refusing to extend Cheek to non-tax criminal statutes), cert. denied, — U.S.-, 113 S.Ct. 416, 121 L.Ed.2d 339 (1992); cf. Ratzlaf v. United States, — U.S. -, -, 114 S.Ct. 655, 663, 126 L.Ed.2d 615 (1994) (not intending to “dishonor the venerable principle that ignorance of the law generally is no defense to a criminal charge” while allowing mistake of law defense in the specific context of criminal prosecutions for violations of the anti-structuring provision of the money laundering statutes).
We see no reason that would prompt us to view heavily regulated air carriers— certified by the FAA and charged with knowledge of the relevant statutes and regulations under which they operate — the same as average citizens who face the daunting task of unraveling the complexities of the Internal Revenue Code. There is cause to be wary because of the ease with which air carriers could fabricate sham defenses and ignore with impunity safety regulations. See United States v. Squires, 440 F.2d 859, 864 (2d Cir.1971) (stating “whenever a defense of ignorance of the law ... is claimed, it is recognized that one may not deliberately close his eyes to what otherwise would have been obvious to him”). Accordingly, when a law, rule or regulation that pertains to pas*819senger and crew safety is clear, we hold that an air carrier — one of the handful of corporations in the business of transporting the public by air — may not claim ignorance of the law as an excuse.
Our holding is narrow. We reiterate it to emphasize its limitations: in a case brought under the Warsaw Convention involving violations of FAA regulations that pertain to the safety of those aboard an aircraft, against a defendant air carrier charged with knowing and following those regulations, that air carrier may not mount a mistake of law defense. In the instant case, therefore, the evidence offered by Pan Am regarding its mistaken view of what was required by the ACSSP was inadmissible for the purposes of mounting a mistake of law defense.
(iii) State of Mind
Notwithstanding the foregoing, appellants insist the oral waiver evidence was admissible on the question of their wilful misconduct, which is of course the ultimate issue in this Warsaw Convention case, see Ospina, 975 F.2d at 37. In Vinieris v. Byzantine Maritime Corp., 731 F.2d 1061 (2d Cir.1984), we addressed the question of admissibility of evidence going to a defendant’s state of mind in the context of a statute that required “conscious misconduct” be proven for a seaman to recover under the penalty provision in a wage-withholding statute. We held that “[n]o evidence which bore even remotely on [state of mind] should have been kept from the jury, unless it interjected tangential and confusing elements which clearly outweighed its relevancy.” Id. at 1064. This formulation is in some sense a restatement of the well-known balancing test contained in Rule 403 of the Federal Rules of Evidence.
Whether the problems to be anticipated by admission of the oral waiver evidence in the present case clearly outweighed the evidence’s relevancy is a close question. Analysis of this issue cannot exist in a vacuum. Because the oral waiver evidence was so intertwined with the government authorization and mistake of law defenses, which as a matter of law were not available to defendants, we believe that admission of such evidence might well have been unnecessarily confusing and perhaps prejudicial so as to justify the trial court’s refusal to allow its admission.
Nonetheless, even were it an abuse of discretion to deny admission of the oral waiver evidence on the foregoing grounds, we hold that such an error was harmless. An eviden-tiary ruling is harmless when we are fairly assured that it had no substantial effect on the jury’s verdict. See Rea, 958 F.2d at 1220. In the instant case, the record is replete with evidence that wholly undermines Pan Am’s claim of good faith. The overwhelming evidence presented during the course of the three and one-half month trial established that Pan Am officials ignored repeated warnings and signals that its security measures were insufficient.
The scope and nature of this evidence needs to be set forth in some detail. We begin in 1983 when a Pan Am flight leaving Rome, Italy for New York was the target of a bomb planted in an unaccompanied interline suitcase. Disaster was averted only when Turkish authorities conducted a passenger/bag match that uncovered the suitcase. Pan Am thus knew of this type of sabotage and that physical matches of suitcases were successful in averting such a terrorist act.
In 1985 a bomb hidden inside a radio and packed in an unaccompanied interline bag exploded on an Air India 747 over the North Atlantic, killing all aboard. The dangers of a bomb hidden inside radios packed in interline bags were well known to Pan Am and the airline industry. These two incidents not only led to the adoption of ACSSP XV.C.l(a), but they conveyed clear warnings that what actually happened at Lockerbie was a distinct possibility.
In September 1986 Pan Am received a report from a group of Israeli security experts commissioned to review Pan Am security at various airports, including Heathrow and Frankfurt. The security experts concluded that “under the present security system, Pan Am is highly vulnerable to most forms of terrorist attack. The fact that no major disaster has occurred to date is merely *820providential.” The report specifically cautioned Pan Am on the use of x-ray machines as substitutes for physical searches, and the dangers of interline unaccompanied bags.
In October 1988 Alert Manager for Germany Ulrich Weber wrote a memo to New York headquarters citing the need for more personnel to remedy Frankfurt’s security shortcomings. Only minimum efforts were made to remedy them.
In July 1988 the FAA issued a Security Bulletin warning of the high threat of a terrorist retaliatory attack because of the downing of an Iranian Jetliner. In November 1988 Pan Am received an FAA Security Bulletin warning that a raid on a terrorist group had uncovered a bomb built into a Toshiba radio cassette player. (Toshiba Warning). The bulletin warned that the bomb was difficult to detect by the use of normal x-ray.
The most wilful disregard of passenger safety, bordering on the outrageous, was in December 1988 when Pan Am received an FAA Security Bulletin advising that the United States Embassy in Helsinki had received a telephone warning that a Pan Am flight from Frankfurt to London and on to New York would be bombed. (Helsinki Warning). The Helsinki warning came just 14 days before the instant tragedy and specifically referred to the Toshiba Warning. Despite these warnings, Pan Am failed to conduct searches of unaccompanied interline luggage, and instead inspected such bags only by x-ray. Pan Am did not even alert x-ray technicians to watch for Toshiba radios. It violated FAA regulations by failing to match the bags with particular tickets without advising the FAA in writing that interline bag match had been discontinued. And it violated other FAA regulations by failing to warn phots about the unaccompanied bags on board for fear that the crews might become “jittery.” Additionally, Pan Am did not replace several members of its security team who were woefully undertrained given their responsibility for thwarting terrorist attacks.
Moreover, the Helsinki Warning was deliberately placed under a pile of papers on the desk of the security officer who received the bulletin and was first discovered in the morning following the downing of Flight 103. There was also evidence that Weber, the security officer in charge, ordered the Pan Am employee who discovered the bulletin after the explosion to backdate the warning to give government investigators the impression that the warning was timely disseminated when received. The district court found that the backdating was evidence of consciousness of guilt on the part of Pan Am for its part in the wrongful causation of the crash.
This and other evidence overwhelmingly supported the jury’s conclusion that but for Pan Am’s wholly inadequate terrorist prevention techniques and its deliberate indifference and overt acts of wilfulness, the bombing and the senseless loss of life would not have occurred. Even had Pan Am been permitted to present Sonesen’s deposition testimony to the jury, the above recited proof, plus the additional fact that any waiver of FAA regulations had to be in writing, make it plain to us that it would not have affected the jury’s finding that Pan Am was guilty of wilful misconduct. Its exclusion was therefore harmless error.
Consequently, for all of the above reasons, the district court’s refusal to permit the admission of Pan Am’s oral waiver evidence— on government authorization, mistake of law, and state of mind grounds — does not constitute a sufficient basis for the granting of a new trial.
B. British Regulations
Appellants’ second contention regarding wrongful exclusion of evidence concerning wilful misconduct relates to British air safety regulations. Appellants sought to introduce British Department of Transportation documents and deposition testimony from James Jack, the Principal Aviation Security Advisor for the British Department of Transportation, in which he explained that Pan Am’s reliance on x-raying interline bags would have complied with British security directives.
With respect to the exclusion of the documentary evidence there was no abuse of discretion. That evidence was proffered in *821the form of British Department of Transport documents and notably included circulars not having the force of law. In addition many of the documents were no longer in effect at the time of the accident. This proof was properly ruled inadmissible as irrelevant, vague, and remote.
The refusal to admit Jack’s deposition is more problematic. The district court stated that it would not admit Jack’s testimony about British regulations unless Pan Am and Alert stipulated that they had violated the ACSSP. Pan Am and Alert understandably refused to make such a potentially prejudicial stipulation. The trial court then suggested that Pan Am and Alert had to choose between claiming they followed the ACSSP or claiming that they violated it, but their wilful misconduct should be judged by local security regulations.
We agree with.Pan Am that it was error to force them to choose between alternate defenses. Alternate and inconsistent defenses are permitted in civil trials. See Fed.R.Civ.P. 8(e)(2); Mathews v. United States, 485 U.S. 58, 64, 108 S.Ct. 883, 887, 99 L.Ed.2d 54 (1988); Kibby v. United States, 372 F.2d 598, 601 (8th Cir.), cert. denied, 387 U.S. 931, 87 S.Ct. 2055, 18 L.Ed.2d 993 (1967). The district court had no authority to exclude evidence on the ground that it supported a defense not consistent with Pan Am and Alert’s alternate theory.
Nevertheless, though it was error to refuse to permit the few pages of Jack’s deposition testimony to be read to the jury, it was harmless error. As we noted above, a ruling is harmless when we are fairly assured that admitting or refusing to admit certain proof had no substantial effect on the jury’s verdict. See Rea, 958 F.2d at 1220. Here the district court did permit Pan Am to adduce some testimony, that its conduct comported with British regulations. The jury had that point before it. Further, plaintiffs’ case rested principally on Pan Am and Alert’s ACSSP violations, not on whether appellants violated British government’s security regulations. The bulk of the evidence regarding the x-ray procedures concerned the issue of ACSSP violations, the importance of conducting a passenger/bag match, and appellants’ purported knowing or reckless behavior in failing to follow FAA regulations.
Moreover, Pan Am and Alert presented a strong defense to the jury that even if they violated the ACSSP, their actions did not amount to wilful misconduct. They insisted that a bomb contained in a suitcasé would have been visible on x-ray. In fact, the parties stipulated to that fact. Appellants’ counsel emphasized in closing argument and elsewhere the safety and expense of the x-ray technology purchased and employed by Pan Am, the fact that even an untrained person could spot a radio on one of their x-ray machines, and made the point that FAA inspections had shown Pan Am x-ray equipment to be in compliance with regulations. Dr. Grodzins, an MIT professor, testified regarding the effectiveness of x-ray examination of baggage. It simply cannot be supposed on the entirety of the voluminous record that Jack’s several pages of deposition testimony would have substantially influenced the verdict, given the fact that the closely related defense that Pan Am presented failed to persuade the jury.
C. “Highest Threat” Evidence
The last of the three wrongfully excluded wilful-misconduct-evidence assertions raised by Pan Am is the court’s refusal to allow evidence that bombs in unaccompanied baggage did not pose the “highest threat” to airline safety. Appellants sought to introduce this evidence to refute the view of one of plaintiffs’ experts that unaccompanied bags pose the greatest risk to airline security-
Pan Am and Alert sought to elicit testimony from their terrorism expert that unaccompanied bags do not pose the highest threat to airline safety; instead, unsuspecting couriers pose that threat. Plaintiffs’ expert, Billie Vincent, had very briefly testified that the unaccompanied bag poses the “highest threat” to airline safety. The defense sought to rebut this position through their expert, Dr. Ariel Merari. They contend Vincent’s testimony left a false impression as to Pan Am’s degree of awareness of the probable *822consequences posed by unaccompanied baggage.
Although the district court did not admit the defense expert’s testimony, it agreed to give an instruction that there was no evidence to show that unaccompanied bags posed the greatest security threat and that the jury should disregard any such opinion. Since such a curative instruction was given, any risk that Vincent’s brief, qualitative testimony was improperly considered by the jury was removed. See, e.g., United States v. Tutino, 883 F.2d 1125, 1137 (2d Cir.1989), cert. denied, 493 U.S. 1081, 110 S.Ct. 1139, 107 L.Ed.2d 1044 (1990). Thus, no abusé of discretion resulted from the exclusion of further testimony on this peripheral subject.
II ADMISSION OF OTHER MISCONDUCT EVIDENCE BY PAN AM AND ALERT AND EXCLUSION OF PAN AM AND ALERT’S ALTERNATIVE SUGGESTIONS OF CAUSATION
Pan Am and Alert’s second major line of argument concerns what it thinks was an error in the trial court’s admitting other evidence of misconduct on their part, while at the same time excluding the testimony of several of their witnesses who, they assert, would have presented alternative theories of causation. We examine each of these challenged rulings separately.
A. Evidence of Appellants’ Alleged Other Misconduct
Appellants complain of evidence received to show other acts of alleged misconduct by the airline.’ This evidence of Pan Am’s and Alert’s other misconduct is divided into two categories — SECURITY VIOLATIONS ON FLIGHT 103 and THE “ALERT” SECURITY PROGRAM. With respect to the former alleged misconduct, the proof was as follows: (1). Ulrich Weber, the head of Alert in Frankfurt had been convicted in the U.S. of passing bad checks eight years before he was hired by Alert and had been fired after the disaster at Lockerbie for using a company credit card in a brothel;' 2) the ramp around Flight 103 had been left unguarded in violation of ACSSP when the Alert employee assigned to guard it felt ill and went inside; 3) Alert employees were inadequately trained, particularly employee Sabine Fuchs who could not explain what a “selectee” was even though her job was to pick “selectees” out from passengers for further screening; one security agent for Flight 103 was an “alternate” who had only two to three hours of training and did not know what the ACSSP required. She thought someone else was monitoring the baggage. 4) Critical to this case is the fact that the x-ray technician for the flight, the only defense against the bomb, had been employed for only seven weeks, had no formal training, and had not been tested. He had never heard about the Toshiba warning.
The proof regarding THE “ALERT” SECURITY PROGRAM revealed first, that it was neither related to security, nor was it a program. Instituted by Pan Am in May 1986 during a period of sharp decline in international travel due to terrorist attacks, the program was a misleading public relations ploy designed to make would-be travelers feel more secure. An advertisement signed by Pan Am’s chairman of the board and CEO was placed in the New York Times and other publications:
Dear Air Traveler:
On June 12, 1986, Pan Am will initiate one of the most far-reaching security programs in our industry, a program that will screen passengers, employees, airport facilities, baggage, and aircraft with unrelenting thoroughness.
The campaign also featured TV ads. As part of the program, Pan Am imposed a security surcharge on international passengers to pay for the promised additional security measures. The surcharge generated $18 million in annual revenue. The security surcharge was $5 each way on overseas tickets — many Flight 103 passengers paid the surcharge— but proceeds from the surcharge were not earmarked for security and instead were commingled with Pan Am’s general funds. Alert’s first president, Fred Ford, wrote a memo to Pan Am senior executives stating that the promised security program was not being put into effect and that passengers would complain “What do I get for my surcharge?”
*823The evidence revealed, second, that Alert added more guards during FAA inspections to make it appear that more guards were on duty than generally was the case; this included on one occasion having a guard from the front end of an airplane sent to the back when FAA inspectors come on board so that the inspectors would think that there was a guard at both places. Third, in 1986 Pan Am declined to adopt security recommendations made to it by the Israeli security consulting firm, KPI, which criticized Pan Am’s reliance on x-ray and emphasized Pan Am’s vulnerability to terrorist attack. Fourth, untrained sniffing dogs had been paraded in front of ticket counters at Kennedy airport to create an appearance of security which did not otherwise exist.
Appellants’ motion to exclude proof not tied to the Air Malta theory of causation (that the bomb bag came from an interline transfer) was denied by the trial court. It observed that since appellants planned to contest the Air Malta theory, plaintiffs were entitled to present evidence of alleged other misconduct on defendants’ parts. The trial judge reasoned that even if the Air Malta theory did not explain the bomb’s presence on Flight 103, other pervasive and extensive wilful misconduct by defendants must have accounted for the bomb’s presence. Following this general ruling, no specific objections were made to the individual pieces of evidence listed above on any other grounds. Other objections that might have been raised were waived. Accordingly, we review this as a general ruling permitting the introduction of evidence showing prior misconduct, unrelated to the Air Malta theory.
This proof that Pan Am acted with wilful misconduct through recklessly disregarding passenger safety in general, with knowledge of the probable consequences of that disregard, was properly received. Although Fed.R.Evid. 404(b) provides for the exclusion of prior misconduct evidence in order to show “character” or action “in conformity therewith”, we follow the inclusionary approach to prior misconduct evidence that allows the admission of prior misconduct for any other relevant purpose. Ismail v. Cohen, 899 F.2d 183, 188 (2d Cir.1990).
Plaintiffs asserted that a contempt for security pervaded Pan Am from the highest to the lowest levels of the corporation, and that the totality of séeurity failures would permit the jury to infer wilful misconduct. We have approved consideration of the totality of a defendant’s wrongdoing in determining whether wilful misconduct existed. See Tug Ocean Prince, Inc. v. United States, 584 F.2d 1151, 1164 (2d Cir.1978), cert. denied, 440 U.S. 959, 99 S.Ct. 1499, 59 L.Ed.2d 772 (1979); see also United States v. Daly, 842 F.2d 1380, 1388 (2d Cir.) (background evidence may be introduced to “furnish an explanation of the understanding or intent with which certain acts [are] performed”), cert. denied, 488 U.S. 821, 109 S.Ct. 66, 102 L.Ed.2d 43 (1988).
Pan Am insists that causation was not established and that therefore the objected to wilful misconduct evidence was speculative and unrelated as a cause of the crash. We think the question of whether it had a causative effect was, without objection or exception, properly submitted to the jury. In other areas of the law, causation may be established when an increasing number of defendant’s faults creates an inference that the totality must have caused the harm. See In Re Marine Sulphur Queen, 460 F.2d 89, 99-100 (2d Cir.), cert. denied, 409 U.S. 982, 93 S.Ct. 326, 34 L.Ed.2d 246 (1972); see also Cappellini v. McCabe Powers Body Co., 713 F.2d 1, 5 (2d Cir.1983) (“decisive consideration in assessing the sufficiency of ... evidence of causation is the ‘relative probability’ of ‘possible explanations’ for the accident, and the ‘legal inferences that can most reasonably be drawn from the most probable ones’”). In libel cases, for example, recklessness causing harm may be demonstrated by cumulative inferences. See Goldwater v. Ginzburg, 414 F.2d 324, 342 (2d Cir.1969), cert. denied, 396 U.S. 1049, 90 S.Ct. 701, 24 L.Ed.2d 695 (1970).
We do not hold that as a matter of law the evidence in this case required the jury to agree with the plausibility of a theory that Pan Am and Alert’s misconduct was so reckless it must have caused the bomb to go undetected. We say only that under the *824Warsaw Convention wilful misconduct causing an accident may be established by inference from the totality of the circumstances. Accord In re Korean Air Lines Disaster of September 1, 1983, 932 F.2d 1475, 1481 (D.C.Cir.) (sufficient evidence existed “from which to decipher a pattern of conduct giving rise to liability"’), cert. denied, — U.S.-, 112 S.Ct. 616, 116 L.Ed.2d 638 (1991).
This conclusion does not mean that any of the burden of proving causation was lifted from plaintiffs. It remained plaintiffs’ duty to prove causation under whatever theory they pursued. In this connection, the district court carefully and in an extensive and well balanced charge instructed the jury that it must find not only wilful misconduct, but also a causal connection between that misconduct and the passengers’ deaths. Chief Judge Platt added that defendants’ conduct would not be proximate cause of the accident if the accident would have occurred anyway, absent defendants’ acts or omissions. Since the evidence introduced by the plaintiffs related to such a showing of causation, there was no error in its receipt.
B. Evidence Challenging Plaintiffs’ Causation Theory
Various attempts by appellants to suggest other specific causation theories were then rebuffed by the trial court. Pan Am and Alert challenge the exclusion of the testimony of four defense witnesses: two offered as experts on terrorism, Noel Koch and Dr. Ariel Merari, and two offered as experts on terrorist bombings, Peter Gurney and John Horne of Scotland Yard. Pan Am also contends it was error to restrict its cross-examination of plaintiffs’ experts, Billie Vincent and Rodney Wallis (the former Director of Security for the International Air Transport Association), with respect to other methods of bombing. The trial judge based his rulings largely on'the fact that he found appellants had offered nothing to show there was any other specific bombing theory.
The admission or exclusion of expert testimony rests soundly in the broad discretion of the trial court. Fed.R.Evid. 702; Hamling v. United States, 418 U.S. 87, 108, 94 S.Ct. 2887, 2902-03, 41 L.Ed.2d 590 (1974); United States v. Gigante, 729 F.2d 78, 83 n. 2 (2d Cir.), cert. denied, 467 U.S. 1206, 104 S.Ct. 2390, 81 L.Ed.2d 348 (1984). That court may, in its discretion,.refuse to entertain expert testimony it thinks unhelpful, cumulative, confusing to the jury, or more prejudicial than probative. See 3 Jack B. Weinstein & Margaret A. Berger, Wein-stein’s Evidence ¶702[02], at 702-18 to -20 (1993). Expert testimony as to causation may be excluded, particularly where it is speculative and conjectural. See Washington v. Armstrong World Indus., Inc., 839 F.2d 1121, 1123-24 (5th Cir.1988) (court within discretion excluding expert’s testimony where expert never examined plaintiff but relied on other expert’s examinations and such testimony as to cause of death was “pure speculation”); Hull v. Merck & Co., Inc., 758 F.2d 1474, 1477-78 (11th Cir.1985) (trial court did not abuse discretion in excluding medical expert’s deposition as to cause of plaintiffs disease because assumptions made seemingly firm opinion speculative and irrelevant); Atlantic Mut. Ins. Co. v. Lavino Shipping Co., 441 F.2d 473, 475 (3d Cir.1971); cf. Novak v. United States, 865 F.2d 718, 722 (6th Cir.1989) (error to rely on expert’s speculation to find causation); Jones v. Goodlove, 334 F.2d 90, 94 (8th Cir.1964) (“[A] trial court may abuse its discretion by allowing a seemingly qualified expert to exceed the permissible bounds of opinion testimony and enter into the realm of utter speculation and conjecture.”).
The trial court did not abuse its discretion in excluding the testimony of defense experts Koch and Merari because their conclusions as to more likely explanations for the bombing were speculative. Any testimony as to some other particular method of bombing — without any foundation that such method might explain the Flight 103 bombing — was clearly conjectural.
Further, appellants admit in their brief that they “did not undertake to prove what method the terrorists used to bomb the aircraft ... [but] contended that the method of bombing has not yet been established.” Because there was no evidence presented with respect to other possible methods of causation that might explain how this tragic event *825occurred, and because appellants never sought to show that any other specific method of bombing could have caused it, any testimony relating to such other causes would necessarily be speculative. Although Dr. Merari and Noel Koch would also have provided general background information on terrorism, the determination whether or not this testimony would have been helpful to the jury rested squarely within the trial court’s discretion. See Fed.R.Evid. 702.
Discretion was also properly exercised in limiting appellants’ cross-examination of plaintiffs’ experts to scenarios that had evidentiary support in the record. Cross-examination of plaintiffs’ experts as to other causation theories — absent a good-faith basis to believe those theories had evidentiary support — was properly excluded. Trial courts possess wide discretion in limiting cross-examination, see N.V. Maatschappij Voor Industriele Waarden v. AO. Smith Corp., 590 F.2d 415, 421 (2d Cir.1978), and here the precluded questions could have drawn the jury into misleading conjecture. Pan Am and Alert were permitted lengthy cross-examination of plaintiffs’ experts, and were only barred from suggesting, without basis, that other scenarios caused the bombing.
It was also not error to decline to receive the testimony of terrorist bombings experts Peter Gurney and John Horne. Their testimony as to the importance of x-rays would have been cumulative since similar testimony was adduced from other witnesses. Additionally, these witnesses’ expertise as to x-rays was questionable. Both witnesses were explosives officers with Scotland Yard who specialized in street bombings. Neither had experience in aviation bombings or security. Moreover, neither had any background or knowledge concerning the Flight 103 bombing itself; the triai court found this rendered their proposed testimony unhelpful and largely irrelevant. This ruling was well within the trial court’s Fed.R.Evid. 702 discretion.
Contrary to appellants’ suggestions throughout .their briefs, Pan Am and Alert were not thereby prevented from presenting a defense on causation. Pan Am and Alert’s summation focused at length and in detail on criticizing plaintiffs’ causation theory; this remained Pan Am and Alert’s main theme throughout cross-examination and their defense case as well. They vigorously attacked major and minor pieces of evidence alike. They were permitted to argue the possibility that a “rush-tag” bag, one by definition sent by the airline apart from its owner, was the unexplained, unaccompanied 13th interline bag x-rayed by operator Kurt Maier in Frankfurt. Importantly, appellants did not offer any fact witness to testify as to another method of bombing that might have caused Flight 103’s crash.
Appellants admit that at trial they sought to argue that the method of bombing was not established and concede they were unable to suggest a specific alternate theory. They vigorously argued that the method of bombing was unclear, and accomplished this through extensive cross-examination of plaintiffs’ experts. Pan Am and Alert also were not deterred from attacking plaintiffs’ weaker theory that widespread misconduct on defendants part more likely than not caused the bomb to be loaded on Flight 103. In sum, Pan Am and Alert exercised the ample opportunities given them to undermine plaintiffs’ causation theory. Thus, the rulings limiting cross-examination and expert testimony were unremarkable and without error.
Ill OTHER EVIDENTIARY RULINGS
While appellants raise an array of objections to other evidentiary rulings — some of which patently involved judgment calls by the trial judge — none of them amount to reversible error.
A. Plaintiffs’ Experts’ Testimony
Appellants’ first objection is to the testimony of plaintiffs’ expert witnesses, Rodney Wallis and Billie Vincent. Walks and Vincent gave their opinions relying on evidence adduced at trial, at times displaying for purposes of reference trial transcripts on a projection screen. Based on this testimony, for example, Wallis opined that Pan Am was operating under a commercial rather than security priority and that training require-*826merits had been violated. Vincent stated— again based on other record testimony — that Pan Am had committed acts that violated ACSSP XV C.l.(a).
Pan Am insists the Wallis and Vincent testimony involved improper summaries of evidence. But the cases relied on for support are inapposite because they do not address experts’ summarizing record evidence, but rather they address summaries of evidence of the sort covered under Fed.R.Evid. 1006. See, e.g., Fagiola v. National Gypsum Co. AC & S., Inc., 906 F.2d 53, 56-57 (2d Cir.1990); United States v. Conlin, 551 F.2d 534, 538-39 (2d Cir.), cert. denied, 434 U.S. 831, 98 S.Ct. 114, 54 L.Ed.2d 91 (1977). Rule 1006 provides in part, “The contents of voluminous writings, recordings, or photographs which cannot conveniently be examined in court may be presented in the form of a chart, summary, or calculation.” It is of some significance that neither Wallis nor Vincent was giving the type of summary testimony that appears on a chart or graph.
The trial judge, therefore, properly ruled on the summary testimony under the federal rules governing expert testimony rather than under Rule 1006. Under those rules, expert testimony may be based on other testimony or evidence obtained at trial. See Fed.R.Evid. 703 (“The facts or data in the particular case upon which an expert bases an opinion or inference may be those perceived by or made known to the expert at or before the hearing.”). No error occurred from the format of testimony summarizing the trial record or from the use of transparencies to highlight portions of the trial transcripts to which the witnesses referred when they were on the witness stand.
Wallis’ and Vincent’s summaries of testimony in the record did not, as appellants assert, improperly impinge on the jury’s functions. Pan Am avers that in assessing other witnesses’ testimony, Wallis and Vincent made credibility judgments that are properly reserved to the jury. They rely for this contention on United States v. Scop, 846 F.2d 135, 142, modified, 856 F.2d 5 (2d Cir.1988). There, it was said in dicta that one witness may not offer an opinion based on his or her assessment of the accuracy of another witness, where that other witness’ credibility is to be determined by the trier of fact. Id. Even were Scop’s discussion of this point binding on us — and it is not — Scop does not in any event, control the outcome of the present case.
Wallis’ and Vincent’s testimonies were not improper simply because they were, based on the testimony of others. Precedent has long acknowledged the acceptability of expert testimony based on the trial record. See, e.g., United States v. Johnson, 319 U.S. 503, 519-20, 63 S.Ct. 1233, 1241, 87 L.Ed. 1546 (1943). No doubt remains under the federal rules that an expert may testify based on facts elicited at trial. See Fed. R.Evid. 703. The rules also provide, “testimony in the form of an opinion or inference otherwise admissible is not objectionable because it embraces an ultimate issue to be decided by the trier of fact.” Fed.R.Evid. 704(a). The credibility of a witness represents just such an ultimate issue normally decided by the jury.
Nor are we troubled by Vincent’s testimony that he thought appellants engaged in “fraud” and “deceit,” because it was clear from the content of his direct and cross-examination that he used those terms in a non-legal sense. Neither do questions arise as to the propriety of testimony given by Wallis, because appellants highlight no specific statement by him containing a legal conclusion as to a specific ACSSP violation. Additionally, because Wallis had an extensive background in aviation security it was not an abuse of the trial court’s discretion to permit him to testify regarding causation.
Pan Am’s next contention has greater merit. It declares that plaintiffs’ witnesses improperly offered legal opinions as to ACSSP violations. We agree that Vincent’s statement as to his beliéf that Pan Am violated the ACSSP is dubious. While an expert witness may testify as to an ultimate fact issue the jury will decide, see Fed. R.Evid. 704, the general rule is that an expert may not testify as to what the law is, because such testimony would impinge on the trial court’s function. See FAA v. Landy, *827705 F.2d 624, 682 (2d Cir.), cert. denied, 464 U.S. 895, 104 S.Ct. 243, 78 L.Ed.2d 232 (1983). Permitting an expert to give a legal conclusion may implicitly provide a legal standard to the jury. See generally Hygh v. Jacobs, 961 F.2d 359, 363-64 (2d Cir.1992); 3 Jack B. Weinstein & Margaret A. Berger, Weinstein’s Evidence ¶ 704[02], at 704-11 to 13 (1993). Thus, expert testimony expressing a legal conclusion should ordinarily be excluded because such testimony is not the way in which a legal standard should be communicated to the jury. Vincent’s testimony that he had been lead to the conclusion “that Pan Am did indeed violate the ACSSP” embodied a legal conclusion that crossed the fine line between a permissible conclusion as to an ultimate issue of fact and an impermissible legal conclusion.
Having said this much, we hasten to add that the introduction of Vincent’s statement was not in our view a reversible error. First, defendants took no specific objection to this statement. By failing to object when the statement was made, the objection was waived. See Fed.R.Evid. 103(a)(1). Second, even had an objection been timely made, the error was harmless. Cf. Hygh, 961 F.2d at 364 (testimony on ultimate legal conclusion found harmless). Vincent’s testimony directly conveyed to the jury that he was stating his own conclusion, it represented but a small portion of extensive testimony providing the basis for his opinion, and the trial judge instructed the jury that it was the ultimate judge of credibility and liability. Under the circumstances, this error — even had there been a proper objection raised — was harmless.
B. Detective Constable Henderson’s Testimony
Scottish Detective Constable Derek Henderson provided deposition testimony as to his work in the Flight 103 investigation. He was assigned responsibility for matching certain bags — the ones that might have been placed in the flight container that was determined to have held the bag with the bomb— with passengers on the aircraft. Henderson prepared his report largely through compiling computerized records of bags. These computerized records had been set up to amass reports from passengers’ and crew members’ friends and relatives, and from evidence obtained at the scene of the crash.
Appellants object to the admission of the detective’s testimony and his report. Based on his analysis of passenger records and information obtained from passengers’ and crew members’ friends and relatives, Henderson determined that the Samsonite bag containing the bomb was an unaccompanied bag from the Frankfurt flight. Defendants moved to exclude his reports as based on multiple’ layers of hearsay; Henderson had compiled his reports based upon other officers’ reports of interviews they had conducted in this necessarily lengthy and involved investigation.
We believe the evidence was properly received under Fed.R.Evid. 803(8)(C), which provides an exception to the hearsay rule for reports of public agencies containing “factual findings resulting from an investigation made pursuant to authority granted by law, unless the sources of information or other circumstances indicate lack of trustworthiness.” See also Beech Aircraft Corp. v. Rainey, 488 U.S. 153, 167, 109 S.Ct. 439, 448, 102 L.Ed.2d 445 (1988) (upholding broad admissibility of facts in government reports, unless circumstances demonstrate lack of trustworthiness). The determination as to any lack of trustworthiness remains one properly left to the district court, id., and its decision to admit a report under Fed.R.Evid. 803(8)(C) is one that we will uphold absent a mánifest error. See Gentile v. County of Suffolk, 926 F.2d 142, 151 (2d Cir.1991).
Here there was no explicit finding of trustworthiness, but no such finding is required before an official report under Rule 803(8)(C) may be received. The plain language of the rule establishes general admissibility, unless a report is deemed to be untrustworthy. See Fed.R.Evid. 803(8) advisory committee’s note; Kehm v. Procter & Gamble Mfg. Co., 724 F.2d 613, 618 (8th Cir.1983). The district court carefully examined the report and did not make a finding of a lack of trustworthiness. Although the trial court did provide a detailed consideration of *828reliability concerns, it had no duty to state it found the report trustworthy.
In any event, adequate evidence demonstrates trustworthiness in the case at hand. The Advisory Committee’s Note on Rule 803(8) suggests several factors to consider in determining trustworthiness: 1) timeliness of the investigation, 2) the investigator’s skill or experience, 3) whether a hearing was held, and 4) possible bias or motivation problems in the report. See Fed.R.Evid. 803(8) advisory committee’s note. The investigation was timely, Henderson was an experienced and skilled, investigator, and no bias may be presumed in the Scottish investigation. We cannot say the trial court abused its discretion in entertaining the report, particularly given its cautionary instructions to the jury concerning the report.
C. X-Ray Demonstration of Radio-Cassette Player
Pan Am and Alert also sought to include an x-ray demonstration as part of their defense to show how clearly a radio-cassette player would appear on the screen. Such a demonstration was ultimately ruled irrelevant, given plaintiffs’ offer to stipulate that a radio-cassette player would be visible on an x-ray screen. Pan Am and Alert nevertheless declare the demonstration would have generally supported Pan Am x-ray operator Kurt Maier’s testimony that he xrayed all the interline bags transferred to Flight 103 in Frankfurt.
The x-ray demonstration would not have either shaken or bolstered Maier’s testimony since he said he could not remember whether any radios or cassette players appeared in any of the bags on Flight 103. More important, because plaintiffs stipulated that a radio cassette player would be clearly recognizable in an x-ray image the proffered demonstration would have been cumulative, and therefore inadmissible' in the district court’s discretion under Fed.R.Evid. 403. When a fact is undisputed and conceded, evidence attempted to be introduced to prove such fact may be excluded. See United States v. Edwards, 631 F.2d 1049, 1051, aff'd, 633 F.2d 207 (2d Cir.1980). Although some cases have upheld the admission of proof respecting a conceded fact, the decision whether or not to do so is a matter that rests within the discretion of the trial court. See, e.g., United States v. Gantzer, 810 F.2d 349, 351 (2d Cir.1987).
IV DAMAGES FOR LOSS OF SOCIETY AND COMPANIONSHIP
Pan Am and Alert’s last claims of error concern the damage awards. In each of the three cases whose damages phases were tried the jury was permitted to award compensatory damages to the decedent’s spouse and children based on the loss of financial contributions, loss of services, loss of society and companionship, and loss of parental care. Appellants do not dispute the awards for the first two elements. But they contend that loss of society and companionship damages are not available under the Warsaw Convention, and that damages for the loss of parental care should not be available to adult children of crash victims.
As we noted in Lockerbie I, damages in a Warsaw Convention case are governed by federal common law principles consistent with the Convention’s terms. Lockerbie I, 928 F.2d at 1278-79; see also Harris v. Polskie Linie Lotnicze, 820 F.2d 1000, 1002 (9th Cir.1989) (“damages are to be measured according to the internal law of a party to the [Warsaw] Convention”). Article 17 of the convention provides for recoveiy of compensatory damages. See Warsaw Convention, art. 17; Lockerbie I, 928 F.2d at 1280-81. The first damages question to be analyzed is whether compensatory damages under the Convention include damages for loss of society and companionship. This question is answered by an examination of maritime law, which is probably the oldest body of federal common law. See In re Mexico City Aircrash, 708 F.2d 400, 414-15 (9th Cir.1983) (looking to general federal maritime law in holding that the Warsaw Convention creates a cause of action for wrongful death).
Appellants agree that maritime law is an appropriate source of law for resolving this issue. But they would have us look only to maritime cases brought under the Death on the High Seas Act, 46 U.S.C.App. §§ 761-*82968 (DOHSA), and the Jones Act, 46 U.S.CApp. § 688, which preclude recovery for loss of society damages. See, e.g., Miles v. Apex Marine Corp., 498 U.S. 19, 31-33, 111 S.Ct. 317, 325-326, 112 L.Ed.2d 275 (1990). General maritime law eases that are not bound by a statutory restriction, in contrast, allow recovery for loss of society. See, e.g., American Export Lines, Inc. v. Alvez, 446 U.S. 274, 280-83, 100 S.Ct. 1673, 1676-1679, 64 L.Ed.2d 284 (1980); Sea-Land Servs., Inc. v. Gaudet, 414 U.S. 573, 585-88, 94 S.Ct. 806, 814-816, 39 L.Ed.2d 9 (1974).
The distinguishing feature in these eases is that the statutes, under which eases precluding loss of society damages have been brought, either expressly limit (DOHSA) or have been interpreted to limit (Jones Act) damages to pecuniary loss. See Mobil Oil Corp. v. Higginbotham, 436 U.S. 618, 620-25, 98 S.Ct. 2010, 2012-2015, 56 L.Ed.2d 581 (1978) (loss of society damages are not recoverable under DOHSA because Congress explicitly limited survivors’ recovery to their “pecuniary losses”); Miles, 498 U.S. at 31-32, 111 S.Ct. at 325 (loss of society damages are not recoverable under Jones Act because in incorporating the Federal Employers’ Liability Act “Congress must have intended to incorporate the pecuniary limitation on damages as well”).
Because we cannot resolve this issue by reference to the common law alone, in light of the conflict between the statutory cases that deny loss of society and the general maritime cases that, along with the majority of states, permit recovery of damages for loss of society, we must look to the Convention itself to determine which of the maritime rules — statutory or general — is most consistent with the language used and the intent of the parties to the treaty. Analyzing Article 17 of the Convention, we look first to its text. The Warsaw Convention has to be evaluated by examining the governing text as drafted in French. See Eastern Airlines, Inc. v. Floyd, 499 U.S. 530, 534-35, 111 S.Ct. 1489, 1493, 113 L.Ed.2d 569 (1991); Air France v. Saks, 470 U.S. 392, 399, 105 S.Ct. 1338, 1342, 84 L.Ed.2d 289 (1985). The English language translation of Article 17 simply provides, in relevant part, “The carrier shall be liable for damage sustained in the event of the death or wounding of a passenger....” The original text of Article 17 provides for compensation for “dommage survenu;” the accepted English language translation of this phrase is “damage sustained.” See Warsaw Convention, art. 17; 49 U.S.C.App. § 1502 note (1988). No limit to pecuniary loss appears in the text. The aim of the Convention’s drafters and signatories appears from the simple language of the text to provide full compensatory damages for any injuries or death covered by the Convention. See In Re Korean Air Lines Disaster, 932 F.2d at 1486-7; Lockerbie I, 928 F.2d at 1281.
While our sources from which to determine the signatories’ intent is limited, scholarly treatises on the subject agree that the French civil law recognized all sorts of damages, pecuniary and nonpecuniary. See In re Korean Air Lines Disaster, 932 F.2d at 1487 (citing G. Miller, Liability in International Air Transport 112 (1977) and R. Mankiewiez, The Liability Regime of the International Air Carrier 157 (1981)). We encountered no understanding in French law that might support limiting “dommage survenu” to exclude loss of society awards.
In light of the broad language in the Warsaw Convention covering “damage sustained” and the lack of authority suggesting that the drafters' wanted to limit compensatory damages to pecuniary loss, we are informed by general maritime law principles set forth in Gaudet and its progeny and hold the Warsaw Convention permits damage awards for loss of society and companionship. Accord In re Korean Air Lines Disaster, 814 F.Supp. 592, 597-98 (E.D.Mich.1993); In re Korean Air Lines Disaster, 807 F.Supp. 1073, 1086-88 (S.D.N.Y.1992). Such holding does not completely dispose of the loss of society damages issue, because the district court did not in any way limit who was entitled to loss of society damages.
Gaudet and Alvez allowed spouses to recover for loss of society. See 414 U.S. at 574, 587-88, 94 S.Ct. at 809, 816; 446 U.S. at 276, 100 S.Ct. at 1674-75. In doing so, the Alvez court noted that this was consistent with the majority of states’ permitting recovery to a wife for loss of consortium, which incorpo*830rates loss of society, from personal injury to her husband. See 446 U.S. at 284, 100 S.Ct. at 1679 & n. 11. Lower federal courts have read these eases to permit dependents to recover as well as spouses for loss of society damages. See Miles v. Melrose, 882 F.2d 976, 989 (5th Cir.1989), aff'd 498 U.S. 19, 111 S.Ct. 317, 112 L.Ed.2d 275 (1990); Sistruk v. Circle Bar Drilling Co., 770 F.2d 455, 458-59 (5th Cir.1985), cert. denied, 475 U.S. 1019, 106 S.Ct. 1205, 89 L.Ed.2d 318 (1986); Anderson v. Whittaker Corp., 692 F.Supp. 734, 770-71 (W.D.Mich.1987), aff'd in part, rev’d in part, 894 F.2d 804 (6th Cir.1990); Truehart v. Blandon, 672 F.Supp. 929, 932-33 (E.D.La.1987), rev’d on other grounds, 884 F.2d 223 (5th Cir.1989). But see DeLoach v. Companhia de Navegacao Lloyd Brasileiro, 782 F.2d 438, 441-43 (3d Cir.1986) (declining to permit dependent child to recover loss of society damages).
We find no maritime case extending loss of society damages to plaintiffs other than spouses and dependents. We therefore affirm the loss of society awards to the Bainbridge and Porter families', since these families consisted of only spouses and dependant children. But the loss of society award to the Pagnucco family must be vacated since some of the family members were adult children and may or may not have been dependents. We remand this limited issue as it applies to the Pagnuccos to the district court for further proceedings consistent with this opinion.
On the issue of damages for lost parental care, we also must vacate and remand all three plaintiffs’ cases to the district court because the district court erroneously instructed the jury on this issue. Damages for lost parental care are considered a pecuniary loss and are therefore recoverable. See Gaudet, 414 U.S. at 585, 94 S.Ct. at 814-15. Appellants correctly contend the district court erred in declining to instruct the jury that damages for loss of fatherly care and guidance must be limited to the period of a child’s minority, absent a showing of specific circumstances that the father’s “guidance had a pecuniary value beyond the irreplaceable values of companionship and affection.” First Nat’l Bank in Greenwich v. National Airlines, Inc., 288 F.2d 621, 624 (2d Cir.1961). Since no such limitation was charged to the jury on this damages issue, the jury awards for loss of parental care may not stand.
On remand, the district court should instruct the jury that it may take into consideration the care, attention, instruction, training, advice, and guidance the evidence shows the father might reasonably have been expected to give his children and to include the pecuniary value thereof in the damages it assesses. The damages for such loss must be limited to the period of a child’s minority, absent a showing of specific circumstances that the father’s guidance had a pecuniary value beyond that period.
CONCLUSION
The record of this trial is not a paradigm of a perfect trial. The critical question though is whether the trial was fair. Here we are satisfied upon an examination of the entire record that defendants received a fair trial. Accordingly, the jury verdicts as to liability are affirmed. However, the award for loss of society damages to the Pagnucco family is vacated as are the awards for loss of parental care in all three plaintiffs’ cases. These cases are remanded to the district court for farther proceedings on the outlined damage issues consistent with this opinion.
. This opinion has been circulated to the active judges of the Court prior to filing. A petition for rehearing of the panel decision filed on January 31, 1994 was submitted on April 6, 1994. After considering the petition, the majority opinion filed January 31, 1994 and the dissenting opinion filed February 18, 1994 were withdrawn and the instant revised majority and dissenting opinions are filed in place thereof. Except to the extent indicated in the revised majority opinion, the petition for rehearing is denied.