BOUDIN, Circuit Judge.

In August 2011, Angel Marquez pled guilty in Massachusetts federal district court to five counts of crack cocaine distribution, 21 U.S.C. § 841(a)(1) (2006); 18 U.S.C. § 2, and one count of conspiracy to distribute, id. § 846. He was sentenced to 121 months in prison and now appeals to challenge the sentence — importantly, the quantity of drugs attributed to him. The facts recounted are taken from the change-of-plea colloquy and the pre-sentence report. United States v. Fernández-Cabrera, 625 F.3d 48, 50 (1st Cir.2010).

In 2009, the FBI targeted the gun- and drug-trafficking businesses of street gangs operating in Lawrence, Haverhill and other cities north of Boston. The FBI relied, in part, on cooperating witnesses' controlled buys of guns and drugs from members of the gangs, which included the Latin Kings, the Latin Gangsta Disciples and the Immortal Outlaws. The buyers were audio- or video-recorded by the FBI in their negotiations with and purchases from the gang members.

In April 2010, one of these cooperating witnesses (whom we refer to as "the CW") drew the FBI's attention to Marquez. The CW told the Bureau that Marquez was a founder of the Immortal Outlaws, had bragged about his acquittal for a murder he committed, and claimed ready access to a supply of both cocaine and crack cocaine. The FBI recorded five drug transactions in which Marquez supplied crack to the CW over the course of five weeks in the late spring and early summer of 2010. Specifically,

In total, the CW purchased 53.87 grams of crack from Marquez for $2,300.

There followed Marquez' arrest, indictment and guilty plea which in turn led to preparation of a pre-sentence report ("PSR"). In the PSR, the Probation Officer attributed not only the 53.87 grams that the CW had bought but also additional drugs to Marquez. Under the "relevant conduct" guideline, a defendant is responsible not only for the wrongdoing to which he pled or of which he was convicted, but also for "all acts and omissions ... that were part of the same course of conduct or common scheme or plan as the offense of conviction." U.S.S.G. § 1B1.3(a)(2); see also id. §§ 3D1.2(d), 2D1.1, 2D1.1 cmt. n. 12.

Relying on recorded conversations with the CW, the PSR concluded that Marquez had acquired at least 152 grams of crack for distribution, including the five sales Marquez made to the CW. Because the recommended guideline sentence is driven in part by drug quantity, Marquez' total offense level ("TOL") for the 152 grams, reduced 3 levels for his guilty plea, was level 25. See U.S.S.G. §§ 2D1.1(c)(6), 3E1.1(a)-(b). This TOL, given his criminal history (calculated as Category IV based on prior convictions), established a recommended guideline sentencing range of 84-105 months. Id. ch. 5, pt. A.

Both sides objected to the PSR. Marquez said that he was responsible for only 53.87 grams, which, when combined with the reduction for his plea, would have given him a TOL of 23 and a range of 70-87 months. U.S.S.G. § 2D1.1(c)(7); id. ch. 5, pt. A. The government urged that the PSR had undercounted and that Marquez' recorded statements made during the drug transactions showed that he had purchased at least two distinct 152-gram supplies of crack. Marquez, while arguing that only the five sales should be counted, said that the transcripts did not establish two 152-gram purchases.

After briefing and argument at the sentencing hearing, the district judge credited the government's interpretation of the transcripts and attributed 304 grams to Marquez. That quantity produced a recommended range of 121-151 months, U.S.S.G. § 2D1.1(c)(4); id. ch. 5, pt. A, and also triggered a statutory mandatory minimum sentence of 120 months, 21 U.S.C. § 841(b)(1)(A)(iii). The judge sentenced Marquez to 121 months — one month above the statutory minimum.

Two of the transcript excerpts bear directly on the amounts of crack handled by Marquez. First, following the May 27 transaction, the CW asked Marquez about his ability to supply a large quantity of crack:

Second, following the June 16 transaction, the CW asked Marquez for details about the size of his drug operation:

On appeal, Marquez first argues that the recordings are insufficient as a matter of law because they were not independently corroborated. Such a claim of legal error is reviewed de novo. United States v. Aguasvivas-Castillo, 668 F.3d 7, 13 (1st Cir.2012). While none of the many cases cited in Marquez' brief establishes a flat corroboration requirement, courts in some cases express doubts, where few details are provided, about the reliability of specific boasts as to past sales or promises of future ones. For example, in United States v. Ruiz, 932 F.2d 1174, 1184 (7th Cir.), cert. denied, 502 U.S. 849, 112 S.Ct. 151, 116 L.Ed.2d 116 (1991), the appeals court found error where the sentencing judge attributed ten kilograms of cocaine to a defendant based solely on his statement, in a two kilogram sale, that "[e]ven ten more I can get."

In varying instances, the law imposes requirements of corroboration, usually meaning only "[c]onfirmation or support by additional evidence or authority." Black's Law Dictionary (9th ed. 2009). Ordinarily, such a rule identifies what is insufficient standing alone.1 Occasionally, some very specific type of corroborating evidence is required to make up the deficit; for instance, the Constitution prescribes that two witnesses are required in trials for treason against the United States. U.S. Const. art. III, § 3, cl. 1.

But in federal sentencing, there is no such flat requirement for proof over and above statements made by a defendant identifying the quantity of a current or proposed drug transaction in which he is involved. On the contrary, recorded statements of defendants are regularly the basis for determinations of drug transactions and drug quantities. E.g., United States v. Figueroa, 976 F.2d 1446, 1450-51, 1460-61 (1st Cir.1992), cert. denied, 507 U.S. 943, 113 S.Ct. 1346, 122 L.Ed.2d 728 (1993). The few circuit cases to address the question squarely — albeit usually in dicta — have said there is no automatic corroboration requirement in the sentencing context. E.g., United States v. Huffman, 461 F.3d 777, 787 (6th Cir.2006), cert. denied, 549 U.S. 1299, 127 S.Ct. 1863, 167 L.Ed.2d 353 (2007).

Of course, the circumstances may, as in Ruiz, persuade a court that a defendant's admission is too thin or too improbable or too likely to be mere boasting to deem it sufficient without more. But to say in that situation that corroboration is "required" is not to invoke a general rule but merely to assess the weakness of that evidence in that case. And Marquez does argue that, even in the absence of a flat rule requiring corroboration, the evidence was insufficient to exceed 53.87 grams.

Both in arguing for 53.87 grams as against the 152 grams recommended by the PSR and in further resisting the 304 figure adopted by the court, Marquez is disadvantaged by the standard of review, for he must show "clear error" by the district judge. Aguasvivas-Castillo, 668 F.3d at 13. Further, the Federal Rules of Evidence do not restrict sources of evidence at sentencing, United States v. Marceau, 554 F.3d 24, 31 (1st Cir.), cert. denied, 556 U.S. 1275, 129 S.Ct. 2752, 174 L.Ed.2d 260 (2009), and the sentencing judge is allowed wide latitude to assess "whether particular evidence is sufficiently reliable," United States v. Cintrón-Echautegui, 604 F.3d 1, 6 (1st Cir.2010). But neither of Marquez' arguments is frivolous.

Unlike the five transactions where Marquez provided crack to the CW and the quantity could be verified by examining the drugs actually seized, the 152 gram figure (or multiple 152 gram figures if the evidence is so taken) related to what Marquez claimed to have acquired for distribution. The term "cop" in the transcripts quoted above is common slang for obtaining drugs; and Marquez himself made clear with some flourishes of detail that what he acquired he broke down into small quantities and resold.

Marquez has on his side several considerations: he gave no detail as to when he acquired the 152 (or 304) grams; he had ample reason, in addition to mere boasting of exploits, to exaggerate to a potential customer his access to drugs; and the amounts he supplied to the CW in the five transactions were a fraction of what he claimed to have received. Whether he had trouble even obtaining the amounts delivered, as claimed by his brief on appeal and disputed by the government, is less certain.

On the other hand, Marquez also said quite clearly that he had copped 152 grams for $2,300 and provided specific details. First, he described a connection to suppliers in Lawrence, who he implied were Dominican. Second, he described the drugs' high quality; his technique for breaking down his supply into smaller amounts for street sales; and, with a possible but minor discrepancy, the amount he supposedly paid for 152 grams. And, of course, he did make five deliveries of increasing amounts to the CW over the course of more than a month.

Nor was the district judge required to view Marquez as a novice making implausible claims. Marquez' criminal history is a long one; in addition to his convictions, there was evidence both from the transcripts and from the CW's report of other statements indicating that Marquez had used guns and had gang connections.2 It was not clear error to conclude that Marquez' then-current and ongoing drug operation included at least one 152-gram purchase.

The finding of two such 152-gram acquisitions is a much closer call. As we read the transcript of the second relevant conversation following the June 16 sale, Marquez was not even arguably describing a particular second 152-gram transaction but instead was responding to the question "how much do you sell on average a week"? The latter, at least, would be a plausible reading of the somewhat blurred and oblique exchange in which Marquez referred on the second occasion to a 152 gram figure. But the government seemingly reads the reference as referring to a second specific 152-gram acquisition and with this we cannot agree.

The district judge's own explanation, unlike the argument of the government, may suggest that he took Marquez to be talking about his general practice rather than a second transaction:

But at this point there is reason to be concerned about treating the second conversation as a sound basis for attributing drugs to Marquez on the basis of an extrapolation theory, even one "conservative" in the period of extrapolation.

Extrapolation is a common and permissible way of attributing drugs to a defendant, see U.S.S.G. § 2D1.1 cmt. n. 12 (instructing courts to approximate drug quantity when necessary); see also United States v. Correa-Alicea, 585 F.3d 484, 489 (1st Cir.2009), cert. denied, ___ U.S. ___, 130 S.Ct. 1909, 176 L.Ed.2d 384 (2010); Figueroa, 976 F.2d at 1460-61. But extrapolation is usually based on a known or readily calculable number of transactions involving clearly established or conservatively estimated quantities. And reliability depends heavily on the predicate figures employed.

In United States v. Webster, 54 F.3d 1, 5 (1st Cir.1995), for example, we upheld a sentence based on a co-defendant's "unequivocal[]" testimony that he supplied the defendant "with one to three ounces of cocaine three times a month for 14 months" and made six purchasing trips to New York with the defendant that "yield[ed] six to twelve ounces of cocaine" (as well as an additional trip that yielded 0.5 kilograms). We upheld the district court in "settl[ing] on two ounces as the per transaction amount for [the defendant's] regular supply and eight ounces as the per trip amount" for the six New York trips because the court adopted "conservative" figures within "relatively tight margins." Id. at 5-6.

But this court has also scrutinized such estimates with care and rejected some as resting too significantly on "unreliable inferences." United States v. Rivera-Maldonado, 194 F.3d 224, 233 (1st Cir.1999). Similar reversals occurred in United States v. Sepulveda, 15 F.3d 1161, 1197 (1st Cir.1993) (witness testified in "sweeping generalities"), cert. denied, 512 U.S. 1223, 114 S.Ct. 2714, 129 L.Ed.2d 840 (1994), and its companion case United States v. Welch, 15 F.3d 1202, 1215 (1st Cir.1993) ("rote averaging" based on lay estimates), cert. denied, 511 U.S. 1096, 114 S.Ct. 1863, 128 L.Ed.2d 485 (1994). Here, the problem is different, namely, whether more than one 152 gram acquisition was ever established.

It is hard to read the broken and garbled exchange in the second conversation quoted above as a reliable estimate of weekly sales or even to be sure that Marquez was admitting that his weekly sales were 152 grams. Marquez had earlier admitted to acquiring 152 grams on one occasion; and he may have been boasting but provided some circumstantial detail. We do not think, however, that any additional 152-gram purchases can be reliably inferred from any further admission.

The district court could conclude that Marquez was in the distribution business and had made sales other than the 152-gram acquisition; but, absent some way of making a reliable estimate of typical quantity, the mechanical assignment of another 152 gram transaction — even though only one more was assigned — has the "dramatic leveraging effect" which concerned us in Sepulveda, 15 F.3d at 1198. Here, it triggered a mandatory minimum sentence in addition to greatly enlarging the recommended guideline sentence.

It is the means of calculating the sentence rather than the result that concerns us. The district judge was entitled on this record to treat Marquez as a more serious offender than one who acquired for distribution only 152 grams even if no precise amount could be estimated, to select the high end of a range so computed or vary upward from it, and to calculate the range itself on the premise that Marquez' criminal history was more extensive than his convictions dictate. But this must be an exercise of judgment rather than drug-quantity formula.

Accordingly, we agree that re-sentencing is required and turn to Marquez' argument that, if a remand is ordered, the district court should be directed to ignore the government's position that his admission to the murder should be considered and that his criminal history category understates the future danger his long record of criminality establishes. The government opposes such a direction and we agree that it would be inappropriate.

Marquez argues that the confession of murder is improper because it is "acquitted conduct"; a jury refused to convict him for the crime of which he boasted. Because the standard of proof is lower in sentencing, the Supreme Court allows the district court to consider acquitted conduct. United States v. Watts, 519 U.S. 148, 156, 117 S.Ct. 633, 136 L.Ed.2d 554 (1997). Nor, as Marquez claims, is this permissible only if the district judge presided over the trial in which the acquittal occurred. United States v. Anonymous Defendant, 629 F.3d 68, 76 (1st Cir.2010).

Whether or not Marquez committed the more than decade-old murder, his long career of crime and his putative gang affiliations, together with his present drug dealing, could well justify something more than the 84-105 months guideline sentence calculated by the PSR. This involves a balancing of the record against claims of rehabilitation put forward by Marquez at sentencing. The district judge did not directly discuss these issues but may find it necessary to do so now.

Marquez argues that gang membership or other indicia of future danger are irrelevant because they are not directly linked to the five drug transactions charged in this case, but this proposed limitation is mistaken. See 18 U.S.C. § 3553(a) (providing that sentencing courts should consider "the history and characteristics of the defendant" and "the need for the sentence imposed ... to protect the public from further crimes of the defendant"); see also United States v. Crawford, 520 F.3d 1072, 1077 (9th Cir.) (considering, inter alia, gang membership), cert. denied, 555 U.S. 960, 129 S.Ct. 433, 172 L.Ed.2d 314 (2008).

The sentence is vacated and the matter remanded for further proceedings consistent with this decision.

It is so ordered.