Defendant-appellant Jonathan Parker was convicted in the United States District Court for the Western District of New York (William M. Skretny, Judge) of killing Leroy Lewis while engaged in a conspiracy to possess with intent to distribute cocaine base. See 21 U.S.C. §§ 841(b)(1)(A), 848(e)(1)(A) (2000). On appeal, Parker challenges the sufficiency of the Government’s evidence, the District Court’s denial of his motion for a new trial, and the admission of supposed lay opinion testimony regarding the circumstances under which drug dealers arm themselves and, specifically, whether a small bulge in Parker’s jacket viewed from a distance was a handgun.
We need not address the motion for a new trial and do not definitively resolve the lay-opinion contentions because, after drawing all reasonable evidentiary inferences in the Government’s favor and mindful that a conviction may rest solely on circumstantial evidence, we nonetheless conclude that no rational trier of fact could have found that the evidence the Government presented proved Parker’s guilt beyond a reasonable doubt.
BACKGROUND
At trial the Government postulated that Parker and Lewis were narcotics dealers and that Parker murdered Lewis in revenge for Lewis’s failure to give Parker an expected share of crack cocaine obtained from the robbery of another narcotics dealer. Specifically, the Government argued that Parker shot Lewis, after discovering that Lewis had lied about the amount of narcotics stolen. During the two-day trial, the Government’s substantive witnesses were three drug dealers, Robert Moore, Klyde Glenn, and McAr-thur Cook, all of whom had extensive criminal histories and had entered into cooperation agreements with the Government. Roshawanda Johnson, Lewis’s girlfriend, testified briefly.
The Government produced no direct or physical evidence establishing Parker as *61the shooter. No eyewitness testified to the shooting. No witnesses testified about any statements concerning the circumstances of the shooting. No DNA or fingerprint evidence was introduced. No evidence was introduced as to Parker’s motive and no murder weapon was found. The Government’s evidence, which was entirely circumstantial, consisted of the following.
From August 1996 until his death on January 13, 1997, Lewis and numerous others regularly dealt crack cocaine in Buffalo, New York in and around the area of Girard Street and Fillmore Avenue. The neighborhood was festooned with drug dealers who openly sold drugs in public in an active drug market. Many of these dealers were familiar with one another, dealt drugs among themselves, and typically were armed or had ready access to various kinds of guns to facilitate their drug dealing.
In connection with his drug dealing, Lewis had a business relationship with an individual named Harry Morris and regularly purchased crack cocaine from Morris for re-sale. In late December 1996 Lewis, along with an acquaintance, Robert Moore, went to the Girard and Fillmore area to meet Morris in an attempt to purchase crack cocaine. When they met Morris, Lewis asked Morris for cocaine but was informed he had none. Parker, an acquaintance of Lewis and also a drug dealer, overheard the conversation and offered to call an individual who could supply drugs to Lewis. Parker then arranged by phone for Lewis to buy crack cocaine from a major drug dealer identified at trial as Calvin Cornelious or “Karl.” Karl subsequently arrived with another individual in a gold Mazda. Parker told Lewis that Karl had a reputation of being “soft” and that, consequently, Lewis could take his drugs without paying. After inconclusive negotiations over drugs, Lewis left the area, retrieved his handgun, and returned. Moore and Lewis then robbed Karl at gunpoint, stole his drugs and his Mazda, and fled the scene. The robbery occurred in plain view of other observers, including drug dealers who frequented the outdoor drug market.
After the robbery, Karl told the group of people who had witnessed it, including Parker, that prior to the robbery he had concealed a half kilogram of crack cocaine in the ear. Another person informed the group that Lewis was involved in the theft. McArthur Cook, who was present for this conversation, testified that he believed Parker heard both statements.
Later that evening Moore, Morris, Parker, and Sidney Barker, another drug dealer, went to Moore’s mother’s house and waited for Lewis. After Morris, Parker, and Barker left, Lewis arrived. Lewis and Moore then went to Lewis’s uncle’s house to divide the stolen drugs. Lewis showed Moore nine ounces of crack cocaine equally divided in two ziplock bags and gave Moore one of them. Moore also saw a third bag fall out of Lewis’s pocket. Lewis and Moore then went to Moore’s mother’s house where they were joined by Parker, who had come to get a share of the stolen drugs. Lewis told Parker that he had stolen only four and a half ounces and that Parker should return the next day for his share of the drugs. Parker returned the next day, and Lewis gave him two quarter ounces of crack cocaine, telling him “that all he had got was four ... ounces and that’s all he was giving him.”
Three days later Parker reappeared and told Moore and Lewis that the Mazda, which was still abandoned, was thought to contain half a kilogram of crack cocaine. The three went to the abandoned car and searched unsuccessfully for additional drugs. No evidence was offered at trial of *62any agreement among Moore, Lewis, Morris, Barker, Parker, or anyone else as to how the stolen drugs would be divided. Nor was proof offered of any arguments or disputes between Lewis and Parker over the division of the stolen drugs.
Lewis was found murdered around 3:00 p.m. on January 13, 1997. Earlier that day, at approximately 1:00 p.m., Parker notified Moore that he wanted to talk to Lewis on Girard Street. Moore relayed this message to Lewis at approximately 2:00 p.m., and they drove to Girard to meet with Parker. Upon arriving, they found Parker in his ear along with another person whom Moore could not identify. After briefly speaking to Parker, Lewis told Moore that he was going with Parker to break into Karl’s house. Lewis also said he would meet Moore in about an hour. Moore saw Lewis enter Parker’s car and saw Parker drive away with Lewis and the other person in the car. Rosha-wanda Johnson, Lewis’s girlfriend, testified that she had a telephone conversation with Lewis between 1:00 and 2:00 p.m. during which Lewis stated that he “ha[d] to make a run” and that “I have to go see my man Face.”1 At some time between 2:00 and 2:30 p.m., Klyde Glenn observed Parker and Lewis seated in a car parked on Fillmore Avenue close to Girard, with Parker in the driver’s seat.
The police received a radio call at approximately 3:50 p.m. reporting a shooting near the intersection of Girard and Fillmore. Police officers arrived a short while later and found Lewis bleeding from what appeared to be a bullet hole in his head. Lewis was taken to Erie County Medical Center and was pronounced dead soon after arrival. An autopsy revealed three bullet wounds to Lewis’s body and determined that the cause of death was a gunshot to the head.
Between 3:00 and 4:00 that afternoon, Cook and Glenn saw Parker walking about four blocks from where Lewis’s body was discovered. Parker called out to Glenn requesting a ride and attempted to attract Glenn’s attention by raising both hands over his head for approximately five seconds. Cook testified that, from a distance of several houses away, he viewed a bulge at Parker’s waist and that, based on his familiarity with guns and his experience with how drug dealers carry guns, the bulge was a handgun and could not have been a pager or any other item.
Glenn agreed to give Parker a ride and, while driving, stated to Parker, “I heard the guy you was [sic] with got shot.” Parker replied that “he didn’t want to talk about that” and asked Glenn to drive him a few blocks to Timón Street. Glenn testified that Parker was calm throughout this conversation and did not appear surprised by Glenn’s revelation that Lewis had been shot. Glenn also testified that as they drove past the site of Lewis’s shooting where police cars and fire trucks had assembled, Parker did not look in that direction.
About three days later, Moore asked Parker what had happened, and Parker responded that “some guy had jumped out [of] the car and shot Leroy.” Moore testified that Parker claimed that the shooter was “Little Ray” and asked Moore to join him so they could find Little Ray and retaliate. Moore also testified that he knew a person named Little Ray, that Little Ray was not the individual he had seen in Parker’s car the afternoon of Lewis’s death, and that he did not believe that Little Ray had shot Lewis.
In March 1997, Parker was interviewed by the Buffalo Police Department as part *63of their investigation of Lewis’s death, as well- as of extensive drug dealing in the area involving Parker, Moore, Glenn, Cook, and the other original defendants in this case. Parker signed a sworn statement in which he made several false statements, principally, that he did not know Lewis, that he was not at the corner of Fillmore and Girard on January 13, 1997, that he had not been to that intersection for approximately one year, and that he had learned of Lewis’s shooting the day after it happened.
The defense did not call any witnesses and, at the conclusion of the trial, moved for a judgment of acquittal on the ground of insufficient evidence. Fed.R.Crim.P. 29. The District Court denied the motion and the jury returned a verdict of guilty. After the verdict, Parker again moved for a judgmént of acquittal pursuant to Rule 29 or, in the alternative, for a new trial pursuant to Rule 33. The District Court denied both motions, noting that “the inconsistencies between the testimonies of Moore, Glenn, and Cook are several, but none of these inconsistencies alone, nor all of them in total, are significant enough to warrant me to override the jury’s verdict or to grant a new trial.” (Transcript, Oct. 26, 2001, at 8.)
The District Court concluded that sufficient evidence existed to support the guilty verdict because “[t]he government produced substantial circumstantial evidence that- defendant killed Leroy Lewis, in particular, that Lewis had shorted defendant on proceeds of a drug robbery, that defendant was the last person seen with Lewis before Lewis was killed, and that defendant was seen running from the general area where the killing occurred, and then requesting a ride away from the area from Glenn.” (Id. at 8-9.) The District Court also rejected Parker’s argument that Cook’s testimony that Parker had a handgun was incredible on its face, finding that, even if the testimony were incredible, “this particular piece of testimony alone is not dispositive of the government’s case.” (Id. at 9.) The District Court concluded, therefore, that no manifest injustice could have resulted. (Id. at 10.) The District Court sentenced Parker to life imprisonment to be served consecutively to a state sentence of life imprisonment that he was already serving. The District Court also sentenced Parker to five years of supervised release and imposed a $100 special assessment.
Parker appealed.
DISCUSSION
I. Standard for Reviewing the Sufficiency of the Government’s Evidence
A defendant challenging the sufficiency of the evidence supporting a conviction faces a “heavy burden.” United States v. Matthews, 20 F.3d 538, 548 (2d Cir.1994). We overturn a conviction on that basis only if, after viewing the evidence in the light' most favorable to the Government and drawing all reasonable inferences in its favor, we determine that “no rational trier of fact” could have concluded that the Government met its burden of proof. United States v. Morrison, 153 F.3d 34, 49 (2d Cir.1998). This standard derives from Jackson v. Virginia, 443 U.S. 307, 99 S.Ct. 2781, 61 L.Ed.2d 560 (1979), in which the Supreme Court instructed that “the relevant question is whether ... any rational trier of fact could have found the essential elements of the crime beyond a reasonable doubt.” Id. at 319, 99 S.Ct. 2781 (emphasis in original). Our evaluation looks at “the evidence in its totality,” and the Government' “need not negate every theory of innocence.” United States v. Autuori, 212 F.3d 105, 114 (2d Cir.2000).
*64“[T]he Due Process Clause protects the accused against conviction except upon proof beyond a reasonable doubt of every fact necessary to constitute the crime with which he is charged.” In re Winship, 397 U.S. 358, 364, 90 S.Ct. 1068, 25 L.Ed.2d 368 (1970). Winship emphasized that the reasonable doubt standard “is a prime instrument for reducing the risk of convictions resting on factual error [and] provides concrete substance for the presumption of innocence — that bedrock ‘axiomatic and elementary’ principle whose ‘enforcement lies at the foundation of the administration of our criminal law.’ ” Id. at 363, 90 S.Ct. 1068 (quoting Coffin v. United States, 156 U.S. 432, 453, 15 S.Ct. 394, 39 L.Ed. 481 (1895)). Because the “Fifth Amendment requirement of proof beyond a reasonable doubt and the Sixth Amendment requirement of a jury verdict are interrelated,” the Constitution requires a jury verdict of guilty beyond a reasonable doubt. Sullivan v. Louisiana, 508 U.S. 275, 278, 113 S.Ct. 2078, 124 L.Ed.2d 182 (1993). “It would not satisfy the Sixth Amendment to have a jury determine that the defendant is probably guilty'....” Id. (emphasis in original); see also Jon O. Newman, Beyond “Reasonable Doubt,” 68 N.Y.U. L.Rev. 979, 989-90 (1993).
Further, notwithstanding the defense’s invitations to the contrary, it is well-settled that when reviewing the sufficiency of the evidence we “defer to the jury’s assessment of witness credibility and the jury’s resolution of conflicting testimony.” United States v. Bala, 236 F.3d 87, 93-94 (2d Cir.2000); accord Morrison, 153 F.3d at 49; United States v. Strauss, 999 F.2d 692, 696 (2d Cir.1993). Consequently, even though each of the Government witnesses (except Johnson) had pled guilty to large-scale drug dealing and testified pursuant to cooperation agreements with the Government and even though their testimony was pock-marked with inconsistencies, at this stage we credit what they said.
Moreover, the absence of any direct evidence that Parker killed Lewis is not dispositive; the prosecution may prove its case entirely by circumstantial evidence so long as guilt is established beyond a reasonable doubt. United States v. Sureff, 15 F.3d 225, 228 (2d Cir.1994) (observing that “a prosecution for murder may succeed without a body having been found or without evidence of the means of death being provided”); United States v. Libera, 989 F.2d 596, 601 (2d Cir.1993); see also United States v. Kwong, 14 F.3d 189, 193 (2d Cir.1994) (holding in an attempted murder prosecution that “[identity can be inferred through circumstantial evidence”). Nevertheless, the record must contain sufficient evidence to support a conclusion that, beyond a reasonable doubt, the defendant committed the crime charged. See United States v. Desena, 260 F.3d 150, 154 (2d Cir.2001); United States v. Nusraty, 867 F.2d 759, 762-64 (2d Cir.1989); United States v. Di Stefano, 555 F.2d 1094, 1103 (2d Cir.1977).
II. The Trial Evidence
With these principles in mind, we review the Government’s evidence. The Government offered some evidence of events prior to the shooting to show Parker’s motive and opportunity to commit the crime. The Government also elicited testimony that, shortly after Lewis was shot, Parker possessed a handgun, departed the general area of Lewis’s death, and reacted casually when informed of the shooting. Finally, the Government showed that about two months after the shooting, Parker made false statements to the police about his activities around the time of the murder. The critical question is whether this evidence, viewed deferentially and in the ag*65gregate, was sufficient to prove Parker’s guilt beyond a reasonable doubt.
1. Parker’s Motive to Kill Lewis
At trial the Government postulated that Parker’s motive to kill Lewis was that Lewis had cheated him out of his share of the stolen drugs. In support of this theory, the Government proved that Parker suggested to Lewis that Karl was “soft” and that Lewis, acting on Parker’s advice, robbed Karl and stole his drugs. According to the Government, Parker felt entitled to a share of the robbery proceeds and visited Lewis later that night “to get his portion of the drugs.” (Transcript, June 6, 2001, pp. 171-72.) Lewis lied to Parker and said that there were only four and a half ounces of crack cocaine even though Karl had told Parker that a half kilogram — about 16 ounces — had been in the Mazda. After Lewis told Parker to come back the next day, Parker again visited Lewis to get his share. Lewis Med again, this time claiming that he had only stolen four ounces. Lewis then told Parker he was only going to give him two quarter ounces “and that’s all he was giving him.” (Id. at 175.) Because Parker had heard Karl say there was a half kilogram of crack cocaine in the Mazda, and because Parker had searched the Mazda after the robbery and found no additional drugs, it is reasonable to infer, the Government contends, that Parker correctly assumed that Lewis was lying about the robbery proceeds and that Parker’s portion of the drugs was unacceptably small. (Id. at 172.)
There were, to be sure, holes in the Government’s proof of motive. The Government failed to estabhsh the existence of an agreement by Lewis to share the stolen drugs with Parker or, for that matter, with Moore or with anyone else. While there was brief, inconclusive testimony that Parker may have hoped for a share of the stolen drugs, there is no proof that he was ever promised anything, and the scant testimony on this topic suggests that the division was determined by Lewis unilaterally, not by agreement. Moreover, the record is bereft of any evidence of disagreement between Parker and Lewis over the distribution of the stolen drugs. There is no evidence that they ever quarreled over the robbery proceeds, that Parker ever threatened Lewis, or that Parker ever complained to Lewis, Moore, or anyone else about the division of the stolen drugs. Nevertheless, we do think the evidence presented was sufficient so that a rational jury could find that Parker had a motive to kill Lewis.
Parker was not unique in holding that motive, however. The Government proved that Lewis was a dishonest drug dealer who robbed a major drug dealer at gunpoint in full view of other drug dealers, their customers, and their associates, stealing a car and a large quantity of crack cocaine. In addition, Moore — another drug dealer whose testimony formed the cornerstone of the Government’s case— testified that Lewis also lied about the amount of drugs stolen when giving Moore his share. Thus, the same assumption necessary to find that Parker had a motive to Mil Lewis would also supply other armed drug dealers with equal if not greater motives.
2. Parker’s Opportunity to Kill Lewis
The Government showed Parker’s opportunity to kill Lewis through evidence that Parker had sought to meet with Lewis prior to the shooting and through the testimony of a witness who observed Parker and Lewis together shortly before Lewis’s death. The value of this evidence, however, was modest for a number of reasons. *66Lewis’s body was discovered near the intersection of Fillmore and Girard, where armed drug dealers and illegal narcotics transactions abounded. For instance, Cook testified that in late 1996, there was “[d]aily drug activity” on the corner of Fillmore and Girard and that he and Glenn sold drugs there.
Further, the Government’s evidence demonstrated that it was not unusual for Parker and Lewis to associate with each other. Moore testified that he had seen Parker and Lewis together five or six times prior to Lewis’s death. Johnson also testified to Parker’s familiarity with Lewis. Finally, Moore testified that there was another unidentified person in the car with Parker shortly before Lewis was shot. Evidence that places Parker with Lewis around the time of the murder is clearly some evidence of opportunity. But the weight of this evidence grows attenuated in the face of evidence that they knew and associated with each other and that someone else besides Parker was seen with Lewis shortly before Lewis’s death.
3. Parker’s Possession of a Handgun Shortly After the Shooting
The Government also offered evidence of Parker’s means to kill Lewis through Cook’s lay opinion testimony, admitted over objection, that a bulge he viewed from a distance of several houses away in Parker’s jacket shortly after the shooting was caused by a handgun.2 Cook testified that between 3:00 p.m. and 4:00 p.m. on the day of Lewis’s shooting, he saw Parker, while walking down the street, raise both hands above his head for approximately five seconds as he called to Glenn to give him a ride in his car. Cook viewed Parker from an estimated distance of five or six houses3 and testified that he perceived a bulge at Parker’s waist that was about three or four inches long and two inches wide.
Cook was then permitted to offer lay opinion testimony about the manner in which drug dealers carry handguns, based on his personal experience in narcotics transactions. Cook explained that a dealer typically carries a larger handgun, such as a .380 caliber gun, by tucking it into his pants at his waist or at the small of his back because the gun is easier to conceal in those locations. Cook then was permitted to opine that, “based on [his] experience on [sic] how people carry guns,” the bulge at Parker’s waist was caused by a gun and could not have been caused by a pager or any other item. (Transcript, June 7, 2001, at 360-61.)
At the outset we emphasize that, under Federal Rules of Evidence 701(c) and 702, this lay opinion was inadmissible and the District Court abused its discretion by admitting it. Rule 701(c) explicitly bars the admission of lay opinions or inferences that are “based on scientific, technical, or *67other specialized knowledge within the scope of Rule 702.” Fed.R.Evid. 701(c). The Advisory Committee explained that the purpose of Rule 701(c) is “to eliminate the risk that the reliability requirements set forth in Rule 702 will be evaded through the simple expedient of proffering an expert in lay witness clothing.” Fed. R.Evid. 701 advisory committee note. That is precisely what happened here.
In the first place, a lay opinion must be “rationally based on the perception of the witness.” Fed.R.Evid. 701(a). This requirement “is the familiar requirement of first-hand knowledge or observation.” United States v. Rea, 958 F.2d 1206, 1215 (2d Cir.1992) (quoting Fed.R.Evid. 701 advisory committee note). Cook observed, from a distance of about five or six houses away, a bulge that he estimated to be only three or four inches long and two inches wide. Based on this observation, Cook conclusively determined that the bulge was caused by a gun, and he was permitted to so testify. But Cook clearly lacked sufficient “first-hand knowledge or observation” to enable him to reach this conclusion. Id.
Secondly, the admission of a lay opinion “based on scientific, technical, or other specialized knowledge” requires that a witness be “qualified as an expert by knowledge, skill, experience, training, or education.” Fed.R.Evid. 701(c), 702. The Government did not offer Cook as an expert witness under Rule 702, and we are confident that Cook would not have qualified to testify as an expert. An expert opinion must be “the product of reliable principles and methods” that the witness has reliably applied to the facts of the case. Fed.R.Evid. 702(2)-(3). Cook did not arrive at his conclusions through reliable principles or methods but through casual, sporadic observations of drug dealers over some unspecified time period. Further, although the Government provided pretrial notice of its intent to offer this evidence as a lay opinion under Rule 701, it failed to provide pretrial notice of expert testimony pursuant to Federal Rule of Criminal Procedure 16(a)(1)(E).
Nevertheless, for purposes of this opinion, we fully credit Cook’s testimony. Even after doing so, however, we find that the combination of this testimony and the remainder of the Government’s evidence is still insufficient to support a conviction. See Lockhart v. Nelson, 488 U.S. 33, 39-40, 109 S.Ct. 285, 102 L.Ed.2d 265 (1988); Burks v. United States, 437 U.S. 1, 18, 98 S.Ct. 2141, 57 L.Ed.2d 1 (1978). The ability of Cook’s testimony about the bulge, even if properly admitted, to carry a circumstantial case was significantly diminished by Cook’s testimony that drug dealers routinely carry guns and that the neighborhood where the shooting occurred routinely included numerous other armed drug dealers. In other words, a sizable inferential leap is required to conclude that Parker must have carried the gun that was used to kill Lewis when no testimony linked Lewis’s killing to Parker’s gun and when others in the immediate area had guns, access to Lewis, and motives to kill him.
4. Parker’s Flight from the Scene
The Government also argued that Parker fled the scene and that this flight evidenced consciousness of guilt. It is well-settled that flight can evidence consciousness of guilt. United States v. Salarmeh, 152 F.3d 88, 157 (2d Cir.1998) (per curiam). But the evidence at trial failed to prove flight. Parker’s supposed flight occurred shortly after Lewis was shot, when Parker attracted Glenn’s attention and requested a ride to Timón Street. Glenn testified that Parker “just threw his hands up in the air [and] just said Shak, that’s *68all.”4 (Transcript, June 7, 2001, at 276.) Glenn then pulled his car over and Parker requested a ride. Cook also testified that Parker was “[w]alking in the street” when he raised his hands and requested a ride from Glenn and that he continued to “walk[] towards” them after lowering his hands. (Id. at 355, 362.) No witness testified that Parker engaged in suspicious conduct while requesting the ride, such as running, aggressively demanding a ride, or requesting to be taken to a remote location. See United States v. Anglin, 169 F.3d 154, 158-60 (2d Cir.1999) (finding evidence sufficient where the Government offered extensive evidence of guilt including proof that the defendant left New York the day after the FBI questioned his close friend about the crime); Salameh, 152 F.3d at 157 (holding that jury could have inferred consciousness of guilt where defendant in a bombing prosecution made arrangements to leave the country the day after the bombing). The court below concluded that sufficient evidence supported Parker’s guilt, in part because “[Parker] was seen running from the general area where the killing occurred.” (Transcript, Oct. 26, 2001, at 9.) The record, however, is devoid of any evidence to support this conclusion.
Glenn testified that Timón Street, Parker’s requested destination, is only four blocks from the intersection of Fillmore and Northampton Street, and the Government offered evidence that Northampton is only a block away from Girard. Thus, the Government’s evidence did not prove that Parker engaged in “flight” and, when added to the balance of its proof, provided little movement toward the reasonable doubt threshold.
Significantly, Glenn — the same witness relied on by the Government to prove flight — testified that, on receiving the ride, Parker behaved calmly. As Glenn drove Parker by the crime scene, Glenn stated, “I heard the guy you was [sic] with got shot.” Parker responded, “I don’t want to talk about that right now.” Parker looked straight ahead and did not turn to look as they passed the police cars and fire trucks at the corner of Fillmore and Girard. The Government argued that this conduct helped prove that Parker killed Lewis; we think it proved little, because the relationship between Parker and Lewis was a subject of brief, inconclusive trial testimony. The Government’s evidence established that Parker and Lewis had, in the past, interacted with each other. Johnson, for instance, testified that Lewis referred to Parker as “my man Face,” and Moore recalled that he had seen Parker and Lewis together five or six times in the past. But we know nothing more. Consequently, even accepting the proposition that Parker’s indifference to the emergency vehicles was odd, the absence of evidence regarding the relationship between Parker and Lewis renders the conclusion that Parker’s indifference resulted from the fact that he had just killed Lewis pure speculation.
5. Parker’s False Exculpatory Statements
Finally, the Government argues that Parker’s false statements to the police following the shooting demonstrated consciousness of guilt. See United States v. Gordon, 987 F.2d 902, 907 (2d Cir.1993) (finding that “circumstantial evidence may include acts that exhibit a consciousness of guilt, such as false exculpatory statements”). Several months after the murder, while being interrogated by Buffalo police, Parker, who was a target of a narcotics investigation, gave a sworn state*69ment that he did not know Lewis, that he was not at the corner of Fillmore and Girard on January 13, 1997, that he had not been to that intersection for approximately one year, and that he had learned of Lewis’s shooting the day after it had occurred. The testimony of several trial witnesses contradicted these statements, and the jury presumably concluded that Parker lied to the police.
Although false exculpatory statements to law enforcement officials may be circumstantial evidence of consciousness of guilt and may strengthen inferences supplied by other pieces of evidence, they do not alone prove guilt. United States v. Samaria, 239 F.3d 228, 236 (2d Cir.2001); United States v. Johnson, 513 F.2d 819, 824 (2d Cir.1975); see also United States v. Nusraty, 867 F.2d 759, 765 (2d Cir.1989) (holding that defendant’s false exculpatory statement was insufficient to support his conviction where other evidence was weak and circumstantial). As we explained in Johnson,
falsehoods told by a defendant in the hope of extricating himself from suspicious circumstances are insufficient proof on which to convict where other evidence of guilt is weak and the evidence before the court is as hospitable to an interpretation consistent with the defendant’s innocence as it is to the Government’s theory of guilt.
513 F.2d at 824; accord Nusraty, 867 F.2d at 765.
In effect, Parker was not willing to admit to the police that he (1) consorted with Lewis, a known drug dealer, (2) frequented a high-traffic drug marketplace on January 13, 1997, and (3) had been frequenting that marketplace for approximately one year. Although Parker’s false exculpatory statements — especially his statement that he had not learned of Lewis’s death until the day after the shooting — unquestionably are probative, their evidentiary value is not, in the context of the remainder of the Government’s case, sufficiently weighty to carry it over the threshold of reasonable doubt.
III. Analyzing the Government’s Evidence in its Totality
We now consider whether, viewing the evidence in its totality and in the light most favorable to the Government, “any rational trier of fact could have found the essential elements of the crime beyond a reasonable doubt.” Jackson, 443 U.S. at 319, 99 S.Ct. 2781. The jury found Parker guilty of violating 21 U.S.C. § 848(e)(1)(A), which provides as follows:
[A]ny person engaging in or working in furtherance of a continuing criminal enterprise, or any person engaging in an offense punishable under section 841(b)(1)(A) of this title or section 960(b)(1) of this title who intentionally kills or counsels, commands, induces, procures, or causes the intentional killing of an individual and such killing results, shall be sentenced to any term of imprisonment, which shall not be less than 20 years, and which may be up to life imprisonment, or may be sentenced to death.
21 U.S.C. § 848(e)(1)(A) (2000). ,In turn, § 841(b)(1)(A), as relevant here, criminalizes possession with intent to distribute and distribution of fifty or more grams of a substance or mixture containing cocaine base. Id. The Government satisfied its burden of proof in regard to certain elements of a § 848(e)(1)(A) conviction by proving that Lewis had been intentionally killed. Additionally, if Parker killed Lewis, the § 841(b)(1)(A) element would have been satisfied because the evidence established Parker’s and Lewis’s involvement in a conspiracy to distribute more than fifty grams of a substance containing cocaine base. The determinative question thus- becomes one of identity, *70namely whether any rational trier of fact could have concluded, beyond a reasonable doubt, that Parker killed Lewis.
Circumstantial evidence can be as compelling as direct evidence and a conviction can rest solely on circumstantial evidence. But the jury must have been presented with a sufficient evidentiary predicate to support the conclusion that, beyond a reasonable doubt, Parker killed Lewis. See Desena, 260 F.3d at 154; United States v. Truesdale, 152 F.3d 443, 448-49 (5th Cir.1998). As the name “circumstantial evidence” suggests, the strength of a particular piece of evidence turns on the specific circumstances that accompany the evidence. Wigmore observed that, “[a]side from autoptic preference,5 [] all evidence must involve an inference from some fact to the proposition to be proved.” See 1A John Henry Wigmore, Wigmore on Evidence § 25 (Tillers rev.1983). But as the inferential leap between the fact and the proposition to be derived grows, the probative value of the evidence diminishes. See Irene Merker Rosenberg & Yale L. Rosenberg, “Perhaps What Ye Say Is Based Only on Conjecture”—Circumstantial Evidence, Then and Now, 31 Hous. L.Rev. 1371, 1385, 1423 (1995).
That occurred here. Jackson requires that a rational juror be able to find the defendant guilty beyond a reasonable doubt, 443 U.S. at 319, 99 S.Ct. 2781, and if the evidence viewed in the light most favorable to the prosecution gives “equal or nearly equal circumstantial support to a theory of guilt and a theory of innocence,” then “a reasonable jury must necessarily entertain a reasonable doubt.” United States v. Lopez, 74 F.3d 575, 577 (5th Cir.) (internal quotation marks and emphasis removed), cert. denied, 517 U.S. 1228, 116 S.Ct. 1867, 134 L.Ed.2d 964 (1996); see also United States v. Andujar, 49 F.3d 16, 20 (1st Cir.1995); United States v. Wright, 835 F.2d 1245, 1249 (8th Cir.1987); Cosby v. Jones, 682 F.2d 1373, 1383 (11th Cir.1982). The Government’s evidence gave “nearly equal circumstantial support” to competing explanations for Lewis’s death: several other drug dealers had equal or substantially more motive to harm Lewis, were armed, had access to Lewis, and frequented the area where Lewis was killed. For these reasons we conclude that the Government’s evidence failed to establish Parker’s guilt beyond a reasonable doubt.
CONCLUSION
The judgment of the District Court is reversed.
. Moore and Klyde Glenn testified that Parker was known as "Face” in the neighborhood.
. Lay opinion testimony is governed by Federal Rule of Evidence 701:
If the witness is not testifying as an expert, the witness’ testimony in the form of opinions or inferences is limited to those opinions or inferences which are (a) rationally based on the perception of the witness, (b) helpful to a clear understanding of the witness’ testimony or the determination of a fact in issue, and (c) not based on scientific, technical, or other specialized knowledge within the scope of Rule 702.
. During direct examination, Cook testified that he viewed Parker from ''[a]bout six houses, five to six houses.” (Transcript, June 7, 2001, at 355.) On cross, Cook explained that he estimated the distance to be the equivalent of five or six houses but, in actuality, five or six houses did not separate them. Rather, the distance consisted of three houses, the width of a street, and a vacant lot. (Id. at 379-81.)
. Glenn testified that his nickname is "Shaka.”
. Wigmore explained that "autoptic preference” refers to "immediate” or "direct” real evidence, in other words, when the thing which is the source of the evidence is present to the sense of the trier of fact. See 1A John Henry Wigmore, Wigmore on Evidence § 24 (Tillers rev.1983).