MORRIS SHEPPARD ARNOLD, Circuit Judge.
Brothers Neng Vue and Lee Vue, who are of Hmong ethnic descent, immigrated from Laos in 1979 with other members of their family. Both were convicted in late 1992 of three drug charges and one firearms charge. The trial court sentenced Neng Vue to 63 months of imprisonment on each of the drug charges and to 60 months on the firearms charge. The trial court sentenced Lee Vue to 41 months on each of the drug charges and to 60 months on the firearms charge.
The Vues appeal both their convictions and their sentences. The government cross-ap[1208]*1208peals the imposition of concurrent, rather than consecutive, sentences on the charges. We reverse the defendants’ convictions, vacate their sentences, and remand the cases for further proceedings. We address, however, several of the issues raised by the Vues that are likely to arise on retrial as well as the issue presented by the government’s cross-appeal.
I.
The Vues, who live in the Twin Cities area of Minnesota, were arrested in fall, 1992, as they left a rented apartment in Sioux Falls, South Dakota, approximately 235 miles from their home. A package had been delivered to that apartment that contained baskets into which raw opium had been interwoven. The delivery was monitored by law enforcement officials. The package, addressed to “Tom Brown” and sent from Thailand, had been taken by Lee Vue inside the apartment building but. was still unopened in the hallway outside the rented apartment when the Vues were arrested. The Vues contended that they had rented the apartment for the use of their brother Fong and two of his friends, Ai Vang and Bee Vang, two individuals who were also immigrants from Laos, according to the Vues. The Vues, disclaiming any knowledge that the package contained opium, asserted that it was the Vangs who had arranged for the package to be sent to the apartment.
The Vues challenge the trial court’s denial of their motion to compel the government to obtain and disclose any information possessed by the Immigration and Naturalization Service (INS) relating to the existence of Ai Vang and Bee Vang. In a related vein, Neng Vue challenges the trial court’s denial of a motion for continuance so that defense counsel could continue to search for the Vangs.
The Vues argue first that INS records relating to the Vangs would have proved the existence of the Vangs, might have helped defense counsel to learn of their whereabouts, and were therefore discoverable as material to the preparation of the Vues’ defense. See Fed.R.Crim.P. 16(a)(1)(C). The Vues contend in addition that such records were exculpatory both because the records were material to the Vues’ guilt or innocence by proving the existence of the Vangs and because the records could have been used to impeach certain government witnesses who were expected to testify that no such persons as the Vangs existed. The Vues also argue, therefore, that the government was required by the constitutional guarantee of due process to disclose those records to the defense. See, e.g., United States v. Bagley, 473 U.S. 667, 676, 105 S.Ct. 3375, 3380, 87 L.Ed.2d 481 (1985), and Brady v. Maryland, 373 U.S. 83, 87, 83 S.Ct. 1194, 1196, 10 L.Ed.2d 215 (1963).
Under both the federal rules and the case law, the Vues must show that the information sought was “material” to their defense. See, e.g., 2 C. Wright, Federal Practice and Procedure: Criminal 2d § 254 at 79 (1982); see also United States v. Cadet, 727 F.2d 1453, 1467-68 (9th Cir.1984). The courts have defined “material” in the context of the federal rules as helpful to the defense. See, e.g., United States v. Krauth, 769 F.2d 473, 476 (8th Cir.1985); see also United States v. Thompson, 944 F.2d 1331, 1341 (7th Cir.1991), cert. denied, — U.S. -, 112 S.Ct. 1177, 117 L.Ed.2d 422 (1992), and United States v. Mandel, 914 F.2d 1215, 1219 (9th Cir.1990). In circumstances where the defense has made a specific request for certain materials, as in this case, the courts have defined “material” in the context of Brady, 373 U.S. at 83, 83 S.Ct. at 1194, as establishing a reasonable probability that suppression of the evidence in question would undermine confidence in the outcome of the trial or, in other words, as establishing a reasonable probability that without suppression of the evidence, the result of the proceeding would have been different. See, e.g., United States v. Bagley, 473 U.S. at 678 (opinion of the Court), 682, 684 (opinion of Blackmun, J.), 685, 105 S.Ct. at 3381, 3383, 3384, 3384 (White, J., concurring) (1985), and United States v. Montoya, 952 F.2d 226, 227 (8th Cir.1991); see also United States v. Bagley, 473 U.S. at 704, 707, 105 S.Ct. at 3395, 3396 (Marshall, J., dissenting); Barrett v. United States, 965 F.2d 1184, 1189 (1st Cir.1992); and United States v. Curtis, 931 F.2d 1011, [1209]*12091014 (4th Cir.1991), cert. denied, — U.S. -, 112 S.Ct. 230, 116 L.Ed.2d 186 (1991).
The trial court never explicitly stated before trial that it did not view INS documents relating to the Vangs as material under either the federal rules or Brady, 373 U.S. at 83, 83 S.Ct. at 1194. The trial court did remark, however, in the final pretrial motion hearing that “whether the defendants rented the apartment, or whether a third party rented the apartment ... does not require us to wait until the government finds Ai and Bee Vang.” We consider those remarks to have functioned as the equivalent of an explicit finding by the trial court that the documents requested were not material.
We have read the transcripts of the three pretrial motion hearings and the trial. We see no abuse of discretion in the trial court’s ruling, nor do we see any reasonable probability that if INS documents on the Vangs had been located and introduced, either of the Vues would have been acquitted. We therefore reject the Vues’ challenge to the trial court’s denial of their motion to compel. See, e.g., 2 C. Wright, Federal Practice and Procedure: Criminal 2d § 254 at 76-77, § 261 at 126-27 (1982). For the same reasons, we reject Neng Vue’s challenge to the trial court’s denial of his motion for continuance. See, e.g., 3A C. Wright, Federal Practice and Procedure: Criminal 2d § 832 at 246-47, 249, 252 (1982).
II.
Lee Vue challenges the trial court’s denial of his motion to suppress a statement that he made to law enforcement officials after his arrest. He argues that his command of English was insufficient for him to understand the explanation given to him of his right to remain silent and his right to a lawyer, that his waiver of those rights was therefore not knowingly and intelligently made, and, accordingly, that his statement was not voluntarily given. See, e.g., Patterson v. Illinois, 487 U.S. 285, 291-93, 292 n. 4, 296-97, 300, 108 S.Ct. 2389, 2394-95, 2394 n. 4, 2397, 2398, 101 L.Ed.2d 261 (1988).
At the pretrial motion hearing on this issue, the trial court stated that “as a high school graduate in the United States, ... Lee Vue would understand the concept of and the words that he wouldn’t have to talk, if he didn’t want to and that he could have a lawyer, if he wanted one, before talking or answering questions.” We have read the transcript of that hearing. The trial court’s findings are not clearly erroneous. See, e.g., United States v. Bordeaux, 980 F.2d 534, 538-39 (8th Cir.1992). We hold, therefore, that the trial court’s denial of the motion to suppress was not improper.
III.
Lee Vue also challenges the trial court’s denial of his motion for severance. That motion was made on the day before the trial began. Counsel for Lee Vue stated in the motion, and again in discussions with the court on the first day of trial, that conversations with Neng Vue’s lawyer had revealed that Neng Vue could provide testimony that would be exculpatory with respect to Lee Vue, that Neng Vue was unlikely to testify in a joint trial, and that Lee Vue had not learned of either of those facts until shortly before he filed the motion for severance. He argued in addition that if Neng Vue were tried separately before Lee Vue was tried, Lee Vue could subpoena Neng Vue and that, having already been tried, Neng Vue would be unable to claim a fifth amendment privilege against testifying. (We express no view on the correctness of that legal proposition.) Lee Vue contended, therefore, that a refusal to sever the defendants’ trials was fundamentally unfair to him and, accordingly, deprived him of due process. See, e.g., Abbott v. Wainwright, 616 F.2d 889, 890 (5th Cir.1980) (per curiam). The trial court denied the motion, stating that where co-defendants are charged with conspiracy in a case involving “virtually a single fact situation,” they are jointly tried in most circumstances.
In reviewing the denial of a motion for severance, we defer to the judgment of the trial court, “absent an abuse of discretion that can be said to have prejudiced the rights of a defendant.” United States v. Foote, 920 F.2d 1395, 1398 (8th Cir.1990), cert. denied, — U.S. -, 111 S.Ct. 2246, 114 L.Ed.2d 487 (1991); see also id. at 1400. [1210]*1210Prejudice sufficient to require severance occurs “when the defendant is deprived of an appreciable chance that he would not have been convicted in a separate trial, and not merely when he would have had a better chance for acquittal in a separate trial.” United States v. O’Meara, 895 F.2d 1216, 1219 (8th Cir.1990), cert. denied, 498 U.S. 943, 111 S.Ct. 352, 112 L.Ed.2d 316 (1990).
“Generally, persons charged with conspiracy are to be tried together.... [N]o error occurs [in denying a motion for severance] when a co-defendant chooses not to testify [in a joint trial] unless it can be shown that the co-defendant would have testified [if the trials had been severed] and that the testimony would be exculpatory.” United States v. Sweeney, 817 F.2d 1323, 1326 (8th Cir.1987), cert. denied, 484 U.S. 866, 108 S.Ct. 189, 98 L.Ed.2d 141 (1987). To require severance, the allegedly exculpatory testimony “should be able to meet and genuinely call into doubt [the government’s evidence] by more than mere denial before the government is required to make separate and duplicative cases against [alleged] co-conspirators.” United States v. Foote, 920 F.2d at 1399-1400.
In the written motion for severance, counsel for Lee Vue asserted, by way of affidavit, that if Neng Vue “were called as a witness on behalf of Lee Vue,” Neng Vue would testify “that Lee Vue was never a party to any agreement to assist in the distribution of ... opium [count 1]; ... that Lee Vue was never in the knowing possession of opium with an intent to distribute it to any person [count 2]; ... that Lee Vue had never previously nor subsequently [to the date of his arrest] ever been involved in the distribution of any controlled substance, nor the interstate travel for purposes of such distribution, and that at the time that Lee Vue left Minnesota for South Dakota that he had no knowledge whatsoever of the package which was eventually seized ... and which contained the opium [count 3]; and ... that at the time that ... Lee Vue left Minneapolis for Sioux Falls, South Dakota, the only purpose for the trip known to Lee Vue was to assist his brother, Fong, in setting up an apartment, and at the time that Lee Vue ... placed [the firearm] in Neng Vue’s car, that Lee Vue had no knowledge whatsoever that any package containing opium existed or would be picked up in Sioux Falls, South Dakota [count 4].” In other cases, we have expressed “serious doubts that a bald assertion by one defendant that he ... will testify as to the innocence of another can be said to be sufficiently exculpatory to mandate severance.” United States v. Foote, 920 F.2d at 1400 n. 3. Those doubts exist even where the testimony would “go to the knowledge or intent element of a crime,” “absent allegations of alibi or like defenses that specifically deny or challenge [other] particular elements of the crime that the government must prove.” Id.
In this case, Lee Vue was able to present his theory of innocence to the jury even though Neng Vue did not testify. In those circumstances, and considering that the allegedly exculpatory evidence would have gone only to Lee Vue’s knowledge or intent, we cannot conclude that he suffered sufficient prejudice in a joint trial that the trial court’s denial of his motion for severance amounted to an abuse of discretion. See, e.g., id. at 1400.
IV.
The firearms offense with which the Vues were charged was using or carrying a firearm “during and in relation to” a federal drug trafficking crime. See 18 U.S.C. § 924(c)(1). The trial court gave two substantive instructions specifically related to that charge. On appeal, the Vues challenge the trial court’s refusal to give two additional instructions proposed by the Vues related to that charge.
The essence of the Vues’ argument is that the law requires the jury to find, first, that the use or carrying of the firearm must be an integral part of the drug trafficking crime and, second, that the use or carrying must be done to facilitate the completion of the crime, or, in other words, that the use or carrying must increase the likelihood that the criminal undertaking will succeed. The Vues contend that those aspects of the law were not sufficiently evident in the instructions given by the trial court.
[1211]*1211We disagree. We see no material difference between an instruction that requires the jury to find that the firearm was “available to aid in the commission” of a drug trafficking crime, as both of the trial court’s substantive instructions were worded in defining the phrase “used or carried a firearm,” and one that requires the jury to find that the firearm was used or carried in order to facilitate the completion of the crime. A recent case, moreover, specifically holds that an instruction requiring the jury to find that the “availability [of the firearm] facilitated the carrying out” of the crime was the equivalent of an instruction requiring the jury to find that the firearm “was an integral part of the crime and increased the likelihood of its success.” See United States v. Michaels, 911 F.2d 131, 132-33 (8th Cir.1990), cert. denied, 498 U.S. 1094, 111 S.Ct. 981, 112 L.Ed.2d 1066 (1991). The trial court’s refusal to give the additional instructions offered by the Vues was therefore not improper.
V.
The Vues challenge the trial court’s admission of certain testimony related to the likelihood of the involvement in opium smuggling of persons of Hmong descent. Essentially, the Vues argue that they were deprived of due process by the admission of the challenged testimony. As will become evident, we consider this issue to be an insurmountable challenge to the Vues’ convictions and therefore recount the questioning and testimony in considerable detail.
During the government’s ease, Michael O’Hara, a customs supervisor for Minnesota, North Dakota, and South Dakota, testified on direct examination about his experience with opium smuggling cases. He referred in his testimony to Operation Oriental Dragon, “a project ... initiated in 1987 to focus on ... a rising amount of opium being smuggled into the Twin Cities from foreign mail branches.” Mr. O’Hara went on to testify that the “opium trade ... in the Twin Cities primarily involves Hmong individuals,” that the “opium is somehow concealed within a parcel shipped from, generally, Thailand,” and that although most of the parcels were initially sent to “legitimate addresses within the public housing of the Hmong community” in St. Paul, he had seen a shift over a five-year period from “public housing addresses” in St. Paul to “more of the outlying areas, counties on the fringe of the metropolitan area,” to “primarily small college towns [within 70 to 90 miles of the Twin Cities area] that had transients.” Mr. O’Hara testified that over a five-year period, his office had participated in “probably ... 100 controlled deliveries [monitored by law enforcement officials] on parcels destined for the Twin Cities area.”
In response to a question asking whether his office had “run into any common problems or techniques” in the controlled deliveries, Mr. O’Hara stated that when his office executed search warrants on the places where the parcels had been sent, “predominantly, most of the time, upon the entries, we [would] find the parcels ... on the premises but not opened.” In response to a subsequent question on “problems you have encountered ... in trying to deliver the boxes,” Mr. O’Hara stated that when “we interview the person that would receive the parcel ... generally, they would ... say, that they didn’t know who the addressee was of the parcel, but accepted it anyway, because it was from Thailand ... [and that] maybe someone else, or some other relative ... might know who this parcel was intended for ... [and that] they didn’t know that the parcel contained opium.”
When Mr. O’Hara was asked if he had encountered, either personally or through the experiences of his office, “any instances where ... the box ... has been opened,” he testified that of the 35 or 40 controlled deliveries in which he had personally participated, he recalled two occasions when “the parcels were actually opened” and that both were “early on,” that is, in 1987 or 1988. In subsequent testimony describing the meeting of law enforcement officials that was held to plan the controlled delivery of the package in this case, Mr. O’Hara stated that he “brought out that based on the experience of the Twin Cities on the delivery of opium parcels to Hmong individuals, that very likely, that the parcel might not be opened even once we [got] into the address with the search warrant.”
[1212]*1212Mr. O’Hara later testified that after he learned that the package had been sent from Thailand and that it contained raw opium, he told an agent of the Drug Enforcement Administration of his suspicion that it was “a Hmong opium smuggling parcel.” The government attorney then asked whether Mr. O’Hara’s suspicion also derived from the fact that the package was coming to the Twin Cities area and whether there were any large ethnic populations in that area “other than the Hmong, where this kind of thing is received.” Mr. O’Hara responded that “there are other populations of individuals from Southeast Asia in the Twin Cities area, but primarily the opium smuggling cases we have identified or we’ve investigated relate to Hmong individuals.” When the government attorney asked for a percentage of the “[o]pi-um smuggling cases in this area” that related to Hmong individuals, Mr. O’Hara stated, “I’d estimate 95 percent.”
Although objection was made to the direct examination testimony related to the likelihood of persons of Hmong descent being involved in opium smuggling, counsel for Neng Vue evidently felt it necessary to try to ameliorate the effect of that testimony by cross-examination on that topic. We do not fault him for doing so in view of the circumstances. We note that as a result, however, the effect of the initial impropriety was magnified, as the following summary makes clear.
Counsel for Neng Vue initially asked, “You stated that based on your knowledge of all the opium being shipped in this area, that approximately 95 percent of that is being done by people of Hmong ancestry, correct?” Mr. O’Hara answered, “The cases within our geographic area of investigative responsibility, which is Minnesota and — and for customs we investigate South Dakota and North Dakota also, but it is Hmong related, correct.” Counsel for Neng Vue then asked again, “[Y]ou say that of all the opium coming from southeastern or southeast Asian countries and surrounding countries, about 95 percent of the opium is being done by Hmong ancestry?” Mr. O’Hara answered, “Opium that’s destined for the Twin Cities area is what I’m referring to is 95 percent Hmong related.”
Counsel for Neng Vue subsequently asked, “Now, you stated based on the fact that the box came from Thailand and was coming to this part of the country, you were able to predict that the Hmongs were likely to be associated with the attempt to transfer these drugs in, correct?” Mr. O’Hara responded, “And also that the box contained baskets with opium interwoven within the baskets, which is consistent with opium type smuggling cases.” Counsel for Neng Vue asked, “Isn’t that also consistent with smuggling type cases from Korea?” Mr. O’Hara answered, “I’ve never encountered an opium smuggling case where the package was shipped from Korea.” When pressed by counsel for Neng Vue as to whether Mr. O’Hara was saying “that’s not possible, that doesn’t happen,” Mr. O’Hara responded, “Anything is possible. It could have been shipped from anywhere, but ... [I] just have no personal experience [myself].” Counsel for Neng Vue asked, “At any rate, you determined that it was — that it was your opinion that the Hmong people were going to be associated with attempting to pick up the opium that was in fact shipped to Sioux Falls?” Mr. O’Hara replied, ‘Tes, that was my belief.”
Counsel for Neng Vue then began asking Mr. O’Hara about a second package that had been identified by customs officials as having been shipped to the Twin Cities area; that package also contained baskets with opium interwoven into them. Mr. O’Hara remarked that he was “not directly involved in that particular case ... but [was] aware that it was delivered.” Counsel for Neng Vue asked, “[T]he particular 100 types of cases that ... you’re aware of concerning shipment of opium to this area of the country, you’re not aware of all the facts in those cases, would that be correct?” Mr. O’Hara responded, “I wouldn’t be aware of specifics, ... but I would know the general facts of the case as to ... the location that it was delivered to and ... that the package was recovered, those kinds of things.” Counsel for Neng Vue added, “And the fact that they’re Hmong people involved?” Mr. O’Hara said, ‘Tes, sir.”
[1213]*1213Counsel for Neng Vue later said, “You stated to the jury on a couple of occasions that you have a lot of knowledge supposedly about the Hmong drug smuggling trade in this area of the country.” Mr. O'Hara then answered, “I’ve worked a number of cases that have involved opium smuggling from southeast Asia which involves Hmongs.”
At least one appellate court has held that the admission of testimony tying the ethnic descent of a defendant to the ethnic characteristics of drug dealers in a specific geographic area or a specific type of drug trade is improper, either because such evidence is irrelevant, see Fed.R.Ev. 401 and Fed.R.Ev. 402, or, even if arguably relevant, because its probative value is outweighed by the danger of unfair prejudice, see Fed.R.Ev. 403. See, e.g., United States v. Doe, 903 F.2d 16, 20-22 (D.C.Cir.1990); see also United States v. Rodriguez Cortes, 949 F.2d 532, 541-42 (1st Cir.1991). We agree that the introduction of such evidence is highly improper.
We have read the transcript of the entire trial. We believe that the evidence was sufficient to sustain the Vues’ convictions. See, e.g., United States v. Jones, 990 F.2d 1047, 1048 (8th Cir.1993). We reverse those convictions (and vacate the sentences), however, because, after having read and reread the transcript of all of the questioning and testimony of Mr. O’Hara, we cannot say either that the error in allowing the introduction of the evidence objected to — the likeli-. hood of the involvement in opium smuggling of persons of Hmong descent — was harmless beyond a reasonable doubt, see, e.g., Delaware v. Van Arsdall, 475 U.S. 673, 684, 106 S.Ct. 1431, 1438, 89 L.Ed.2d 674 (1986), and Chapman v. California, 386 U.S. 18, 24, 87 S.Ct. 824, 828, 17 L.Ed.2d 705 (1967) (errors of constitutional magnitude), or that we do not have grave doubt with respect to whether the outcome of the trial was substantially influenced by the introduction of that evidence, see, e.g., Bank of Nova Scotia v. United States, 487 U.S. 250, 256, 263, 108 S.Ct. 2369, 2374, 2378, 101 L.Ed.2d 228 (1988), and Kotteakos v. United States, 328 U.S. 750, 765, 776, 66 S.Ct. 1239, 1248, 1253, 90 L.Ed. 1557 (1946) (errors not of constitutional magnitude). See also 3A C. Wright, Federal Practice and Procedure: Criminal 2d § 854 at 300-11, § 855 at 325-35 (1982), and Fed. R.Crim.P. 52(a).
We believe that the error here was indeed of constitutional dimension, because the injection of ethnicity into the trial clearly invited the jury to put the Vues’ racial and cultural background into the balance in determining their guilt. We view this as a serious trespass on the rights to due process and equal protection guaranteed to the Vues by the fifth amendment. Formal equality before the law is the bedrock of our legal system, and we are determined that that principle will not be undermined.
VI.
The trial court ordered that the sentences on all four counts of conviction for each defendant were to run concurrently. The government cross-appeals that order insofar as it applies to the imposition of a sentence on the firearms charge that would run concurrently with the sentences on the three drug charges. Although we have vacated the Vues’ sentences for the reasons given above, we add this section of our opinion to make clear that we agree with the government that the trial court lacked the authority to order the sentence on the firearms charge to run concurrently with the sentences on the drug charges.
As noted earlier, the firearms charge of which the Vues were convicted was using or carrying a firearm “during and in relation to” a federal drug trafficking crime. See 18 U.S.C. § 924(c)(1). That statute also provides that, “[notwithstanding any other provision of law, the court shall not place on probation or suspend the sentence of any person convicted [under] this subsection, nor shall the term of imprisonment imposed under this subsection run concurrently with any other term of imprisonment including that imposed for the ... drug trafficking crime in which the firearm was used or carried” (emphasis supplied). Id.
In spite of the unqualified language of the statute, the trial court did make the sentence on the firearms charge concurrent with the sentences on the drug charges. We are un[1214]*1214certain why it did so. (During the sentencing hearing, the trial court gave no reason for its ruling. In an order denying the government’s motion for a reconsideration of the ruling with respect to concurrent sentences, the trial court stated only, “It is the view of the court that it is appropriate and in order to reach a fair sentence, that the sentences on each count be served concurrently.”)
As far as we can tell (and the Vues have cited no contrary authority), every appellate court that has considered this question has ruled that a trial court has no discretion to ignore the directive for consecutive sentences that the statute contains. See, e.g., United States v. Lanzi, 933 F.2d 824, 826 (10th Cir.1991); United States v. Lawrence, 928 F.2d 36, 38-39 (2d Cir.1991); United States v. Garrett, 903 F.2d 1105, 1114 (7th Cir.1990), cert. denied, 498 U.S. 905, 111 S.Ct. 272, 112 L.Ed.2d 227 (1990); United States v. Van Dyke, 895 F.2d 984, 985-87 (4th Cir.1990), cert. denied, 498 U.S. 838, 111 S.Ct. 112, 112 L.Ed.2d 82 (1990); and United States v. Hunter, 887 F.2d 1001, 1002-03 (9th Cir.1989) (per curiam), cert. denied, 493 U.S. 1090, 110 S.Ct. 1159, 107 L.Ed.2d 1062 (1990). We so hold as well.
VII.
For the reasons stated, the Vues’ convictions are reversed, their sentences are vacated, and the cases are remanded for further proceedings.