On September 3, 1998, a jury returned a verdict against José Ramón Hernández-Rodríguez (“Hernández”), finding him guilty of five offenses associated with conspiracy to import, possess, and distribute a large quantity of cocaine. His co-defendant, Douglas Gorbea-Del Valle (“Gor-bea”) was also convicted. Hernández was sentenced to five concurrent terms of imprisonment, each 293 months in duration. He filed a timely appeal, and this court affirmed the conviction and sentence on July 17, 2000. United States v. Hernandez, 218 F.3d 58 (1st Cir.2000), cert. denied, 531 U.S. 1103, 121 S.Ct. 840, 148 L.Ed.2d 720 (2001).
On July 29, 2002, Hernández filed a Motion for a New Trial under Fed. R.Crim.P. 331 (“Rule 33”) alleging that he was misidentified and offering newly discovered evidence. Two years later, in June 2004, a magistrate judge issued a Report and Recommendation that Hernán-dez be granted a new trial. On December 22, 2004, the district judge rejected the magistrate’s recommendation and denied the motion for a new trial.
Hernández herein appeals from the district court’s denial of his motion for a new trial. Because we find that the. district court erred both in its analysis of the new evidence and insofar as it rejected the magistrate’s credibility determination without first hearing the evidence, we reverse the district court and remand the case for action consistent with this opinion.
I.
On September 27, 1997, U.S. Customs officials intercepted a container at Crowley Yard in San Juan, Puerto Rico. It had just arrived from Venezuela, and although the bill of lading indicated that the container held only plastic cups, there was contraband inside as well. The consignee was a *141supermarket, and the consignee’s representative was South Atlantic Trading Company (SATCO), of which Gorbea was part owner. Customs agents unloaded 7,514 pounds of cocaine, worth nearly one billion dollars. They then re-packed the containers with approximately 24 pounds of cocaine.
On October 2, driver Alain Ruiz-Galin-dez (“Ruiz”),2 an employee of J.R. Transport — a company owned by Hernández— arrived at Crowley Yard to retrieve the container. The truck stopped several times during its route, sometimes for thirty minutes or more. A trip that the district court judge estimated should, have taken thirty minutes took about four hours. Although other cars on the road at that time had their headlights on, Ruiz drove without headlights. From the moment the truck left Crowley Yard, Hernán-dez followed it in a gray van. During one of the stopovers he exited the van and entered the truck, where he remained until it arrived at J.R. Transport’s truck yard. At some point, the van stopped following the truck.
It appeared to the officers, following the truck that a Crown Victoria with several passengers inside arrived at the truck yard at the same time as the truck, and that one passenger carried an object that might have been a gun. The officers reported seeing people in the truck yard greeting and congratulating one another once the container was inside the lot. After surveying the scene, the officers moved in and made arrests. The container had not been opened.
When Gorbea was arrested in December 1997, a faxed document was found in his briefcase (“the fax”). It was dated February 5,1997 — nearly ten months prior to his arrest and almost eight months - before the container was intercepted — from a Marina Kassert in Venezuela regarding an earlier shipment of plastic cups. It said, “I urgently need the information of your friend that has the truck to square everything with him.” On the back of the two-page fax, among several other handwritten notes, was the name José Hernandez.
At their joint trial, neither Gorbea nor Hernández presented any evidence and both were convicted on September 3, 1998. Ruiz, also a defendant, was acquitted. After this court affirmed his conviction, Hernández, 218 F.3d at 71, Hernández filed a 28 U.S.C. § 2255 petition claiming ineffective assistance of counsel. Hernández v. United States, No. 97-228, 2004 WL 1737361, *2 (D.P.R. June 29, 2004). In that petition, Hernández specifically pointed to' his attorney’s failure to interview Gorbea, alleging that such an interview would have revealed exculpatory evidence. Id. at *2. His § 2255 petition was denied in June 2002. Id. On July 29, 2002, Hernán-dez filed a Motion for a New Trial under Fed.R.Crim.P. 33, alleging newly discovered evidence and innocence.
The new evidence was an affidavit from Gorbea, declaring that he and Hernández did not know each, other personally until they met, after their arrest, in a detention facility in Puerto Rico. According to his affidavit, at the time of his arrest Gorbea told U.S. Customs agents Ricardo Rivera (“Agent Rivera”) and Brenda Talavera (“Agent Talavera”) that he did not know Hernández personally, and the agents took note of this information. Id. at *4. At the evidentiary hearing before the magistrate judge, Gorbea testified that he never told Hernández about the drugs in the truck, and that because no one in Venezuela knew Hernández either, Hernández had “no reason to know” of the drugs in the *142container. Id. at *5. Gorbea testified that he never told truckers what they were hauling, and — although he did not admit his own guilt — he explained that if he were to import drugs, he would never inform the truckers because he would need to pay them extra otherwise.3 Id. Gorbea also testified that he chose to use J.R. Transport only because its rates undercut those of the other trucking companies he had considered. Id. For his part, Hernández testified that he had only one telephone conversation with Gorbea prior to their arrest, and that conversation pertained only to the negotiation of his fee for transporting the cargo.4 Id. Under the agreed terms, Hernández had transported two shipments of plastic cups prior to the final shipment, at issue in this case. Id.
Of particular significance was Gorbea’s testimony regarding the fax. At the evi-dentiary hearing, he explained that in May 1997 (approximately three months after the fax transmission) he was in Venezuela looking for information regarding a shipment of soda crackers that was scheduled to go to Puerto Rico from Venezuela. Id. at *6. Gorbea stated that he called the company representing Crowley Maritime Shipping in Venezuela and spoke to an individual by the name of José Hernández-Avilés, or some similar name, who was unable to help him. Id. That employee transferred him to two or three other people at Crowley in Puerto Rico until Gorbea found someone who knew when the container was due to arrive. Id. Gorbea testified that the person who finally provided the information he needed was called José Hernández, and that he wrote the name on the back of the fax paper as he was being transferred from one person to the next. Id. Finally, Gorbea stated his belief that Defendant Hernández was not the individual to whom he spoke on the phone that day. Id. at *1. He explained that if he had been referring to Defendant Hernández, he would have known and used Hernán-dez’s nickname, “Papito,” or the name of his company, “J.R. Trucking.” Id.
After filing for a new trial but before the evidentiary hearing, Hernández moved to compel Crowley Maritime Corporation to produce personnel records regarding the existence of any employees with the name José Hernández during the time period in question. The records indicate that from May to October 1997, the following were Crowley employees: 1) José Hernández-Vélez (San Juan); 2) José Hernández-Marrero (San Juan); 3) José Hernández-Febus (San Juan); 4) José Hernández (Venezuela).
At the evidentiary hearing, the government presented the testimonies of Agents Talavera and Rivera. Agent Talavera testified that she went to Crowley as part of her investigation to determine whether José Hernández had ever worked there. Although she did not remember the outcome of the inquiry, she stated her belief that knowledge of a Crowley employee by the same name in Venezuela would have been “important and significant” to her investigation. Id. at *8. Similarly, Agent Rivera testified that he did not personally verify whether a person with the name José Hernández worked at Crowley, and when asked whether such information *143would have been important to his investigation, he replied “[w]ell, now it is. Perhaps back then it wasn’t.” Id. at *9.
Agent Talavera was asked to describe the evidence — aside from the fax — of Her-nández’s willing and knowing participation in the crime. Id. at *8. Agent Talavera responded with the following: employees of J.R. Trucking obtained the paperwork for the shipment and moved the container which held the drugs; a surveillance video recorded Ruiz walking around the truck prior to departure, inspecting the seal, the locks, and the tires; agents following the truck saw Hernández and Ruiz periodically getting out of the truck to examine it from behind during the unusually long journey from Crowley Yard to "the J.R. Trucking yard; and the truck drove without headlights. Id. Agent Talavera testified that she had no knowledge of whether the truck had mechanical problems, but the magistrate judge found that Agent Talav-era’s report clearly contained the driver’s explanation as to his circuitous route: the truck had no serviceable lights and he used the back roads so as to avoid police detection of the fact that the truck was driving without lights. Id.
Of note is Hernández’s testimony at the evidentiary hearing regarding Agent Ta-lavera’s summary of the evidence against him. Hernández explained that when a trailer is made available for pickup it has already been cleared by U.S. Customs, and thus the fact of his company having transported the container is not intrinsically incriminating because he was misled by the government as to the legality of the container’s contents. He also shed light on the driver’s behavior as Talavera described it, saying that once the driver receives a container for pickup, the trailer is sealed and the driver is not permitted to break the seal under threat of penalty. Id. at 20. The driver must also conduct an external inspection of the truck, checking the tires and inspecting the seal. Id.
II.
Our standard of review of a district court’s denial of a Rule 33 motion for a new trial is “manifest abuse of discretion.” United States v. Falú-González, 205 F.3d 436, 442 (1st Cir.2000). The issue before us on appeal is thus whether the district court abused’ its discretion when it found the newly proffered evidence insufficient to warrant a new trial under Rule 33.5
We use a four-part test to evaluate a request for a new trial on the’basis of newly discovered evidence. Id. The defendant bears the weighty burden “to establish that ‘the evidence was: (i) unknown or unavailable at the time of trial, (ii) despite due diligence, (iii) material, and (iv) likely to result in an acquittal upon retrial.’ ” Id. (quoting United States v. Montilla-Rivera, 115 F.3d 1060, 1064-65 (1st Cir.1997)).
The district court did not analyze the first two prongs, finding that Hernández could not surmount either- the third or fourth part. We will consider appellant’s claim with respect to the test in its entirety, cognizant of our own precedent which dictates that we have no discretion to grant a motion for a new trial if any one of the four factors is lacking. United States v. Natanel, 938 F.2d 302, 313 (1st Cir. 1991).
Hernández claims, and the magistrate judge agreed, that the new.evidence *144proffered in this case — Gorbea’s affidavit — was unavailable at the time of trial. This circuit has long held that exculpatory affidavits from co-defendants who exercised them Fifth Amendment privilege not to testify at trial may constitute “newly discovered evidence” for Rule 33 purposes. Montilla-Rivera, 115 F.3d at 1065-66. Contra United States v. Theodosopoulos, 48 F.3d 1438, 1448 (7th Cir.1995); United States v. Muldrow, 19 F.3d 1332, 1339 (10th Cir.1994). Nevertheless, we have also emphasized the need for “great skepticism” in such cases because “[a] convicted, sentenced codefendant has little to lose (and perhaps something to gain) by such testimony.” Montilla-Rivera, 115 F.3d at 1066. Thus, although we are satisfied that the new evidence in this case was unavailable at trial — and thus sufficient to satisfy the first prong of Montillch-Rivera — we proceed through the remainder of the inquiry with the appropriate caution.6
The district court assumed arguendo, without further discussion, that the defendant established due diligence. The magistrate, however, considered the issue and found persuasive an affidavit by Hernández’s counsel in response to Hernández’s unsuccessful § 2255 motion in which he detailed his efforts to solicit Gorbea’s testimony at trial. Hernández, 2004 WL 1737361, at *12. He stated that in pretrial meetings with both defendants and their counsel,
it was agreed that Defendant Gorbea would take the stand and testify in a way favorable to both him and Hernán-dez. However, when the government rested its case Gorbea had made up his mind, and refused to testify although his counsel had advised him to do so and explained to him that the defense needed his testimony to convey to the jury the fact that the defendants had no knowledge at all about the presence of cocaine in the container.
Id.
A survey of the circuits reveals that the requisite measure of diligence in a Rule 33 inquiry is dependent upon the nature of the evidence in question. See, e.g., United States v. Villarreal, 324 F.3d 319, 326 (5th Cir.2003) (finding that defendant was not sufficiently diligent where the new evidence proffered consisted of details in a video that was introduced at trial, and which would have been visible had the tape been played more slowly); United States v. Alessi, 638 F.2d 466, 479 (2d Cir.1980) (observing that defendant should have been more diligent in attempting to obtain a letter — offered after conviction as the basis of a Rule 33 motion — the existence of which he had been aware at trial).
We find that the diligence factor — where the new evidence in question is the testimony of a co-defendant who exercised his Fifth Amendment privilege at trial — does not require more than Hernández has shown in this case. He did not have the power to compel Gorbea to waive the privilege against self-incrimination, and since both defendants and their counsel agreed in pretrial meetings that Gorbea should and would testify, it seems certain that Hernández’s diligence burden has been discharged. Hernández has thus satisfied the second prong of Montilla-Rivera.
*145The district court found that the new evidence, even if unavailable at trial despite Hernández’s exercise of due diligence, was not material. We have long held that a showing of materiality is essential to a successful Rule 33 claim on the basis of new evidence. United States v. Wright, 625 F.2d 1017, 1019 (1st Cir.1980). The district court’s materiality analysis was confined to its determination that, “as the fax pertains to a different time period and shipment, though supportive in establishing the present conspiracy, it is logically unnecessary, and hence immaterial.” Hernández v. United States, 350 F.Supp.2d 340, 345 (D.P.R.2004).
Although the district court correctly points out the seven month gap between the date of the fax (February 5) and the interception of the shipment at issue in this case (September 27), we find the materiality analysis to have been too limited. New evidence is material if it has the potential “to alter the outcome of the lawsuit under the applicable legal tenets.” Roche v. John Hancock Mut. Life Ins. Co., 81 F.3d 249, 253 (1st Cir.1996).7 Hernández was convicted of conspiracy. The bulk of Gorbea’s affidavit and testimony speaks directly to the question of whether Hernández knew or had reason to know that there were drugs in the container. This alone, in our opinion, would be sufficient to satisfy the materiality element. As for Gorbea’s testimony regarding the fax, despite the seven month delay between the fax and the shipment, we clearly stated in our affirmance of his conviction that “[o]f great weight is the fact that Gorbea wrote Hernández’s name on the back of the fax” because it suggested the existence of conspiracy at an earlier date. Hernandez, 218 F.3d at 67. Furthermore, we find significant the fact that in its closing argument at trial, the gqvernment made specific reference to. the fax, asking the jury, “[n]ow, ladies and gentlemen, why does a shipper in Venezuela need the name of the trucker in Puerto Rico, to square what?” Hernández, 2004 WL 1737361, at *15. And in its rebuttal the government argued:
The fourth count deals only with Mr. Douglas Gorbea and Mr. Hernández and that is a conspiracy to import and what is the evidence there. Mr. Gorbea, as early as March, starts importing paper cups and who is his friend and trucker, Mr. J.R. In government’s Exhibit 11, the telefax, Mr. Gorbea unites in his own handwriting, Juan Hernández and what is Marina Kassert asking him, give me the name of your' trucker, your friend. So now you know that Mr. Hernández had participated in that importation and that the importation did succeed.
Id. (emphasis added). The government specifically told the jury that the fax constituted evidence of at least one count with which Hernández was charged and ultimately convicted. Gorbea’s alternative explanation for the name on the fax, coupled with new corroborating evidence of multiple employees with the same name work*146ing at Crowley during the time period in question, goes directly to Hernandez’s claim of misidentification. Thus, we find that Hernández has satisfied Montillar-Rivera’s third prong.
Finally, Hernández must demonstrate that the new evidence is “likely to result in an acquittal upon retrial.” Falu-González, 205 F.3d at 442 (quoting Montilla-Rivera, 115 F.3d at 1064-65). The district court began its analysis with a statement that it would assume, arguendo, that the defendant’s proffered evidence is credible. Hernández, 350 F.Supp.2d at 344. The court nonetheless held that Hernández has not made a sufficient showing under this prong because
[w]hile there may be other explanations for the truck’s evasive route, and even for the name written on the fax, “[a] reasonable jury could infer [petitioner’s] knowledge of the contents of the container and his participation in the larger scheme,” from his suspicious behavior in transporting the container, to wit, tailing the truck in a van for four hours, when it should have taken an unaccompanied truck driver no more than a half hour.
Id. at 345 (quoting Hernández, 218 F.3d at 58). Similarly insurmountable, in the district court’s view, are the “celebration which ensued in petitioner’s truck yard upon the arrival of the container” and “the fact that the container was taken to the J.R. Transport lot, rather than directly to [Gorbea’s premises].” Id. (internal citation and quotation marks omitted).
The district court considered the primary value of the defendant’s new evidence to be Gorbea’s suggestion of an alternative explanation for the name written on the fax. We think, however, that this assessment fails to account for the full implications of the new evidence. If the jury were to believe Gorbea’s affidavit and testimony at a new trial, it would find that: Hernández and Gorbea did not know one another personally prior to arrest; Gorbea never spoke to Hernández about transporting drugs and gave Hernández no reason to think that he was transporting anything but ordinary cargo that had cleared U.S. Customs in the ordinary fashion; Gorbea never mentioned Hernández to anyone in Venezuela; Gorbea only hired Hernández to haul the container because he was the lowest bidder for the job; and the name on the back of the February 5 fax referred to an altogether different person.
Inasmuch as the district judge failed to consider the full import of the defendant’s new evidence, we conclude that the district court abused its discretion. As we view the evidence in this case, if deemed credible by a jury, Gorbea’s testimony would greatly undermine the conspiracy charges against Hernández. The government relied heavily on the theory that Hernández and Gorbea were close and trusted partners in establishing its case against Her-nández. In addition to the government’s other comments regarding the contents of the fax, for example, the government emphasized to the jury that “[t]his is not Garcia Trucking, this is J.R. Trucking. So the plan, you see, for this deception go[es] way back. This did not happen over night because the people in ... Venezuela ... are not going to send [the cocaine] to anybody ... They are going to send it to somebody they know, somebody they can trust, somebody who is responsible to them, if something happens.” The government premised its case against Hernández on the notion that the people in Venezuela who shipped the cocaine wanted Gorbea to choose a trusted friend to transport the shipment once it arrived. If the jury were to believe Gorbea’s testimony that he and Hernández had no such relationship prior to their arrest and that he never told any *147of his contacts in Venezuela about Hernán-dez, the government’s theory begins to unravel. To prove conspiracy, the government must demonstrate “the existence of a conspiracy, the defendant’s knowledge of the conspiracy, and the defendant’s voluntary participation in the conspiracy.” Her-nández, 218 F.3d at 64-65 (internal citation and quotation marks omitted). Given the government’s emphasis on the importance of Hernández’s close relationship with Gorbea, Gorbea’s testimony would go to the heart of each showing.
In a new trial, the government would be left to contest Gorbea’s credible testimony (so assumed by the district court) with the circumstantial evidence of the truck’s long route, the strange behavior of the defendant and the drivef, and the celebration that ensued upon the truck’s arrival. The district court placed great weight on this circumstantial evidence in its analysis, relying on our assessment of the sufficiency of the evidence on direct review. However, a determination on direct review that certain evidence is sufficient to support a verdict does not eliminate the possibility that, if new evidence is later presented, a court may grant a motion for a new trial. Indeed, we have previously stated that where the government’s case against a defendant is “sufficient, but underwhelming,” new, credible testimony “could lead to a different outcome.” Montillar-Rivera, 115 F.3d at 1066. On direct review, we determined that the circumstantial evidence presented against Hernández was sufficient to support the guilty verdict when viewed in the light most favorable to the government. Hernández, 218 F.3d at 67 & n. 6. However, we also acknowledged that, “[a]s with much of the evidence in this case, the record provides other possible explanations for the[ ] facts” regarding the “suspicious” transport of the container. Id. The record shows that the jury heard testimony from a government witness that Ruiz, Hernández’s employee and driver of the truck, had explained that the truck was experiencing electrical problems, including the loss of headlights, and that he chose to drive-on back roads because of those problems. The jury also heard' testimony that witnesses had observed what appeared to be a battery generator hooked up to the truck. These electrical problems could explain the truck’s use of back roads and frequent stops. The eventüal “celebration” in the truck yard could be merely a congratulatory exchange regarding the safe arrival of a disabled truck. At the very least, this alternative explanation calls into question the strength of the government’s circumstantial evidence.
In considering the motion for a new trial, we must carefully consider the strength of the government’s case in light of the new evidence. In so doing, we find it difficult to understand how the govern-mént’s circumstantial evidence could so overwhelm the direct testimony of Gorbea (that the district court assumed was credible and which, by its terms, undermines the government’s theory that Gorbea and Hernández were conspiring to transport the drugs) as to preclude a likelihood of acquittal upon retrial.
To the extent that the district court’s denial of the motion for a new trial may have been influenced by a negative assessment of Gorbea’s- credibility, there was another error in the judge’s ruling. Despite the district court’s strong suggestion to the contrary, Hernández, 350 F.Supp.2d at 344, we find that Gorbea’s testimony and credibility were of great import in the disposition of this case because we think a reasonable jury would not convict Hernán-dez- if it were to find Gorbea’s testimony credible. The Supreme Court has held that a district judge need not hear the live *148testimony of a witness in order to accept the credibility determination of a magistrate judge. United States v. Raddatz, 447 U.S. 667, 680-81, 100 S.Ct. 2406, 65 L.Ed.2d 424 (1980). However, the Court left open the question of whether a district judge may reject a credibility determination of a magistrate without first hearing the testimony. Id. at 681 n. 7 (“[W]e assume it is unlikely that a district judge would reject a magistrate’s proposed findings on credibility ... [T]o do so without seeing and hearing the witness or witnesses whose credibility is in question could well give rise to serious questions which'we do not reach.”).
Although we have not previously addressed this question, a few other circuits have had occasion to consider it, and they are in broad agreement: A district judge may not reject a magistrate’s findings as to the credibility of a witness without hearing the witness testify first-hand. See United States v. Cofield, 272 F.3d 1303, 1306 (11th Cir.2001); Hill v. Beyer, 62 F.3d 474, 482 (3d Cir.1995); Louis v. Blackburn, 630 F.2d 1105, 1109 (5th Cir. 1980).
Today we join our sister circuits when we find that, absent special circumstances, a district judge may not reject the credibility determination of a magistrate judge without first hearing the testimony that was the basis for that determination. Thus, to the extent that the district court’s analysis rested upon the rejection of the magistrate judge’s credibility determination without hearing the testimony, the district court abused its discretion.
III.
In summary, we conclude that the district court abused its discretion by failing to consider the full import of defendant’s new evidence given its decision to assume, arguendo, Gorbea’s credibility. Furthermore, to the extent that the district court’s analysis rested upon the rejection of the magistrate judge’s credibility determination without hearing the evidence, it abused its discretion. In light of these errors, we remand for further proceedings.
In considering this case, however, we are faced with a dilemma as to whether we should remand to a different district judge. This dilemma arises because it will become necessary for the district court, if it chooses not to accept the credibility findings of the magistrate judge on remand, to hear Gorbea testify first-hand and make its own credibility determination. Although we believe that, upon remand, the district judge in this case would conduct the necessary proceedings with impartiality, we are concerned here with the possible appearance of injustice. The district judge in this case assumed the credibility of the evidence and then concluded, in error, that a new trial was not warranted. If, upon remand, the same district judge were to conduct a hearing (rather than accept the magistrate’s credibility determination) and find that the testimony was not credible, it might appear that his determination was improperly influenced by his initial decision. As one of our sister circuits observed in a factually similar case, “[t]here are occasions when a matter is appropriately remanded to a different district judge not only in recognition of the difficulty that a judge might have putting aside his previously expressed views, but also to preserve the appearance of justice.” Cullen v. U.S., 194 F.3d 401, 408 (2d Cir.1999) (internal citation and quotation marks omitted). We find that this is such an occasion.
For the foregoing reasons, we remand this case to a different district judge for proceedings consistent with this opinion.
Remanded.
. "Upon the defendant's motion, the court may vacate any judgment and grant a new trial if the interest of justice so requires.” Fed.R.Crim.P. 33(a).
. Ruiz was tried jointly with Gorbea and Her-nández, but was acquitted on all counts.
. By contrast, Hernández testified that he agreed to charge twenty percent below market rate in order to secure the job with Gor-bea. Id.
. We do not understand this testimony to be inconsistent with Gorbea's statement that the two only "met” after they were both in custody because Gorbea seems clearly to refer to the first meeting in which more transpired than simply a negotiation between a common carrier and a consignee regarding a shipment of plastic cups.
. Hernández also raises a separate entrapment claim, apparently for the first time in his brief on this appeal. We do not address it because "[t]heories not raised in the district court cannot be raised for the first time on appeal.” Tobin v. Liberty Mut. Ins. Co., 428 F.3d 54, 59 n. 3 (1st Cir.2005).
. In his dissenting opinion, Judge Howard expresses concern about whether Gorbea’s testimony should be accorded significant weight in light of the fact that Gorbea has not admitted guilt. As Montilla-Rivera requires, we have considered this evidence with "great skepticism." Nevertheless, we disagree with Judge Howard’s conclusion that Gorbea's testimony, even if deemed credible, would fail to undermine significantly the government's case against Hernández.
. Although the materiality standard set forth in Roche was actually used in the summary judgment context, we have borrowed it here because we have not previously defined evi-dentiary materiality in this context, and we find it to be apt.
We have defined materiality where the Rule 33 motion is based on an alleged Brady violation. Conley v. United States, 415 F.3d 183, 188 (1st Cir.2005) (“The suppression of impeachment evidence is material when a reasonable probability exists that the result of the trial would have been different if the suppressed documents had been disclosed to the defense.”) (internal citation and quotation marks omitted). However, there is a slight difference between the Rule- 33 analysis within the Brady context and outside of, it, and we have not herein adopted the Conley definition of materiality because it would be difficult to reconcile with the fourth prong of the Falú-Gonzalez test that controls here.