
593 F.3d 115 (2010)
UNITED STATES, Appellee,
v.
Halvor CARL, Defendant, Appellant.
No. 08-2281.
United States Court of Appeals, First Circuit.
Heard November 2, 2009.
Decided January 29, 2010.
*116 Robert C. Andrews, for appellant.
Margaret D. McGaughey, Appellate Chief, with whom Paula D. Silsby, United States Attorney, was on brief for appellee.
Before LYNCH, Chief Judge, STAHL, Circuit Judge, and DiCLERICO,[*] District Judge.
DiCLERICO, District Judge.
The defendant, Halvor Carl, appeals his conviction and sentence following a jury trial in the district court. Carl was convicted on Count 6 of the Indictment, which alleged distribution of cocaine base in violation of 21 U.S.C. §§ 841(a)(1) and (b)(1)(C). He was sentenced to 120 months in prison and to 3 years of supervised *117 release. On appeal, Carl argues that the district court erred by admitting certain statements at trial, improperly calculating the drug quantity for purposes of sentencing, and including acquitted conduct in the presentence report. For the reasons that follow, we affirm the judgment of the district court.

I.
During the end of October and beginning of November 2004, two men robbed and burglarized several business establishments in Cumberland and York Counties, Maine. Following an investigation, law enforcement officials identified Bryan Black and Timothy Riley as suspects and obtained a search warrant for Halvor Carl's mobile home in Buxton. Around midnight on November 6, 2004, a team of Maine law enforcement officials executed the warrant by surrounding the home and phoning Carl to request that the people within leave voluntarily. When Carl came out of his home, he was told to kneel and was restrained with flex cuffs. No Miranda warnings were given at that time.
Donald Foss, a detective lieutenant with the Cumberland County Sheriff's Office, was the first officer to speak with Carl. Preparing to take Carl to a nearby command post, Foss patted Carl down and asked him his name. Carl answered and then asked, "Why aren't you arresting the real robbers?" Foss inquired, "Who is that?," to which Carl replied, "Bryan [Black] and Timothy [Riley]." Carl also told Foss that Black was hiding in Carl's home and Riley had a gun and was at a nearby motel with Marylou Frisco, who was Bryan's sister and Carl's live-in girlfriend. Carl said that Timothy would not come to Carl's home because Carl would "beat his ass."
Two Gorham police officers then took Carl to the Buxton Police Department. At the station, he was advised of his Miranda rights, and he signed a waiver of his rights. An officer told him he was free to leave, but he spoke with two policemen for an hour.
In early March 2005, Carl left a message with the U.S. Attorney's Office indicating that he had information about the 2004 robberies. On March 8, he was interviewed by Special Agent Michael Grasso of the Bureau of Alcohol, Tobacco, Firearms, and Explosives (ATF). Carl told Agent Grasso about the involvement of Black, Riley, and Frisco in the robberies, but he refused to provide information about himself without an attorney. Shortly after receiving a grand jury subpoena a few days later, Carl requested and received court-appointed counsel.
On March 14, 2007, a federal grand jury indicted Carl, Black, and Frisco for the robberies.[1] The indictment also included one count against Carl of distributing cocaine base (crack). Carl was arrested on May 31, 2007, in Virginia, by ATF Special Agent Kurk Broksas, as well as by a Secret Service agent and a deputy U.S. Marshal. When Carl was in custody, he received Miranda warnings but stated that he was willing to answer questions without an attorney. During an interview with Agent Broksas, Carl made several incriminating statements, including an admission that he had sold cocaine to Riley and Black and had possessed 0.33 gram of cocaine in New Hampshire and 14 grams of cocaine in Maine. Carl mentioned that he was represented by counsel, in the context of explaining why he had fled to Virginia. Specifically, he said that his attorney told him that if Carl were convicted on pending state charges, he could then be prosecuted *118 on federal charges and might be considered a career criminal, which would increase his sentence. At no time during the interview did Carl request to speak to his appointed attorney or any other attorney.
Carl was tried in federal district court from April 28 to April 30, 2008. During the trial, Riley, Frisco, and Black all testified about the drugs they bought and received from Carl. Riley stated that Carl was his heaviest supplier, who sold Riley several "hundred-rocks" of freebase cocaine.[2] Frisco testified that she received both crack and powder cocaine from Carl beginning on her second date with him, in July 2004, and that she smoked cocaine Carl had supplied all day, every day toward the end of October and beginning of November 2004. Black recalled that he used cocaine with Carl within fifteen minutes of being introduced to him. The three cooperating witnesses also testified that there were several other people who came to Carl's home during the period from August to November of 2004 both to purchase and to use cocaine.
Detective Foss and Agent Broksas also testified briefly at Carl's trial. Foss recounted the statements that Carl made to him on the night of November 6, 2004, that Black and Riley were the real robbers, that Black was in Carl's home, that Riley had a gun and was at a motel with Frisco, and that Riley would not go to Carl's home because Carl would assault him. Broksas testified that Carl told him that he had gone to Virginia to avoid prosecution in Maine and New Hampshire on state drug charges. Broksas also recalled Carl's admissions about possessing and selling cocaine. During closing arguments, the prosecutor mentioned Carl's confession to Broksas about selling drugs to Riley and Black, but did not discuss Foss's testimony.
Carl was acquitted of the robbery charges but convicted on the single count of distributing cocaine base, in violation of 21 U.S.C. § 841(a)(1) and (b)(1)(C). His sentencing hearing was held September 22, 2008, during which Riley, Frisco, and Black, pursuant to their plea agreements, testified again about the drugs they had received from Carl. Riley stated that he bought at least one fifty-rock from Carl every day for two weeks, and that the total was between 7 and 14 grams of crack. Frisco said she began dating Carl in July of 2004 and that he gave her at least 1 gram of powder and 2 grams of crack each day from that point until November 6, 2004, with the exception of only thirteen days. She also recounted several trips with Carl both in and out of state to purchase either small amounts of crack or between 1 and 5 ounces of powder cocaine. Black said he purchased about $17,000 worth of crack from Carl over the period in question. He recalled receiving at least 2 grams, or as much as two or three eight-balls each day, as well as five or six eight-balls on a single day in October. Black remembered accompanying Carl on trips to Massachusetts and New Hampshire during which Carl purchased a total of 9 or 10 ounces of cocaine.
Carl's counsel vigorously cross-examined all three of the cooperating witnesses, both at trial and sentencing. He pointed out that they were long-time drug addicts who *119 were hoping, by testifying, to receive reductions in their sentences.
Based on the witnesses' testimony, the court found that Carl was responsible for distributing a total of 579.5 grams of crack and 106 grams of powder cocaine. Applying the Sentencing Guidelines, the court determined that the amount was equivalent to 11,611.2 kilograms of marijuana, which resulted in a base offense level of 36. This level was reduced to 34 under U.S.S.G. § 2D1.1 Commentary Note 10(D)(i). Carl's criminal history category was I. The court found that the guideline range was 151-188 months. After considering the presentence investigation report (PSR), the evidence and arguments offered by counsel, Carl's short allocution, the seriousness of the offense, and the need for deterrence, the court sentenced Carl to 120 months in prison and 3 years of supervised release.

II.
Carl raises four issues on appeal. He contends that the district court erred in admitting at trial the statements he made to Agent Broksas in Virginia, and that this error violated his Sixth Amendment right to counsel. Carl argues that the court also erred in admitting the statements he made to Detective Foss, which violated his Fifth Amendment right against self-incrimination. With regard to sentencing, Carl argues that the court erred in relying on the testimony of drug-addicted cooperating witnesses in finding the amount of drugs for which Carl should be held responsible. Finally, Carl asserts that the district court failed to resolve a dispute over the inclusion of acquitted conduct in the PSR, and that failure to do so could cause the Bureau of Prisons to classify him incorrectly.

A. Sixth Amendment Claim

Carl argues that his Miranda waiver at the outset of the May 31, 2007, interrogation was ineffective because his attorney was not present, and that therefore his Sixth Amendment right to counsel was violated. He acknowledges that the waiver was knowing and voluntary and that he did not explicitly request an attorney at any time during the interview. He argues, however, that he invoked his right to counsel during his March 8, 2005, interview with Special Agent Grasso and that this invocation barred any resumption of interrogation by any official about the same crime.[3]
We do not reach the merits of Carl's claim that his Sixth Amendment right to an attorney was violated because we find that if any error occurred, it was harmless. "[W]e will not reverse a conviction because of trial error in admitting evidence obtained in violation of a defendant's Sixth Amendment right to counsel if the error was `harmless beyond a reasonable doubt.'" United States v. León-Delfis, 203 F.3d 103, 112 (1st Cir.2000) (quoting Milton v. Wainwright, 407 U.S. 371, 372, 92 S.Ct. 2174, 33 L.Ed.2d 1 (1972)).
In order to determine whether an error was harmless beyond a reasonable doubt, we consider a number of factors, including "the importance of the challenged *120 statement in the prosecution's case, whether the statement was cumulative, the presence or absence of evidence corroborating or contradicting the statement on material points, the extent of cross-examination otherwise permitted, and the overall strength of the prosecution's case." United States v. Earle, 488 F.3d 537, 546 (1st Cir.2007). When weighing these factors, we are mindful that a defendant's confession "[is] by nature highly probative and likely to be at the center of a jury's attention." León-Delfis, 203 F.3d at 112.
Agent Broksas testified that Carl told him that he had gone to Virginia to avoid being prosecuted on state drug charges, that he had sold cocaine to Riley and Black, and that he had possessed 14 grams of cocaine in Maine and 0.33 gram in New Hampshire. Even if Agent Broksas's testimony had been excluded, other evidence proved that Carl was distributing cocaine base. Riley, Frisco, and Black each testified repeatedly about the drugs Carl provided to them.
Carl was Riley's "heaviest supplier of crack," who helped Riley smoke "constantly" during the two or three weeks leading up to November 6. Riley testified that Carl gave him and Black crack just before the two burglarized a store in Limington, Maine. Riley discussed purchasing hundred-rock after hundred-rock from Carl, and seeing many other people in Carl's house smoking crack. He said that the first time he met Carl was at Riley's mother's house, where she, her fiancé, and Carl were smoking crack. Riley also explained that he gave the proceeds of his crimes, including the three November robberies in Gorham, Buxton, and Hollis, Maine, directly to Carl to pay for drugs.
Frisco testified that Carl gave her crack on her second date with him, and that he continued to do so through November 6. Her account of smoking "every day, all day" in late October and early November, and observing Riley doing the same thing, matched Riley's statement. Frisco told the jury that her brother, Bryan Black, was Carl's customer, and that her other brother, Michael Frisco, purchased marijuana and pills from Carl, in addition to cocaine. She testified that Riley's mother and her fiancé were "frequent customers" of Carl's, which was consistent with Riley's testimony. Frisco also confirmed the fact that the proceeds from the three robberies were paid to Carl in exchange for crack. In addition, she said that she was upset that Carl's home, where she was staying with her three children, "looked like a 7-Eleven with so many cars [belonging to drug customers] out front." Frisco described taking between ten and twenty trips with Carl to purchase cocaine, including purchases from his daughter in New Hampshire, a man in Sanford, Maine, and individuals in the Riverton Park area of Portland.
Black said that he paid Carl for cocaine using both the income Black earned at legitimate construction and masonry work and the proceeds of various burglaries and the November robberies. Black described going with Carl to buy crack three times: twice to Manchester, New Hampshire, and once to Sanford. Black, like the other two witnesses, described seeing Carl distribute crack to other customers "numerous times."
Carl's attorney cross-examined Riley, Frisco, and Black at length about their testimony, their criminal histories, and their drug use. Each witness described prior convictions, many years of drug use and, in Riley's case, mental health disorders. Carl's attorney also brought out the witnesses' cooperation with the prosecution under the terms of plea agreements and questioned whether they were lying in order to get Carl convicted and, in turn, *121 receive reductions in their sentences for assisting the prosecution.
In comparison to the lengthy, detailed testimonies of Riley, Frisco, and Black, Agent Broksas's testimony about Carl's statement was brief. He told the jury that Carl confessed to selling and possessing cocaine. Carl's attorney examined Broksas about his training in questioning suspects, and Broksas admitted that he did not tape-record his interview with Carl, which would have provided a more faithful account of Carl's statements than the report Broksas wrote the day after the interview. He also acknowledged that Carl might have used words that differed slightly from those Broksas put in his written report.
The primary and most important evidence of Carl's extensive drug activities came from Riley, Frisco, and Black. Their testimony strongly corroborated Carl's confession as reported by Broksas. Unlike Broksas's summary of Carl's confession, which was cursory and lacked detail, the testimony of Riley, Frisco, and Black included many details of specific drug sales. Further, although the prosecutor mentioned Carl's confession in closing argument, she focused on the drug evidence provided by these three witnesses.
While we do not minimize the fact that a confession is generally considered important evidence of guilt, in this case the weight to be accorded to the confession was lessened through cross-examination, and, importantly, other substantial evidence corroborative of Carl's guilt was presented to the jury. Taking into account all of the evidence adduced at trial, we conclude that, even if the district court erred in admitting Carl's confession, which we doubt, any error was harmless beyond a reasonable doubt.

B. Fifth Amendment Claim

Carl asserts that the district court erred by admitting the statements he made to "detectives" on the night of November 6, 2004. The only such statements admitted at trial were those made to Detective Foss, and those are the statements we will review.
Carl argues that the admission of his statements violated his Fifth Amendment rights because the police did not administer Miranda warnings before Carl's interaction with Foss, and they delayed the warnings until Carl reached the Buxton police station.
As with the statements Carl made to Agent Broksas in Virginia, we do not reach the issue of whether Carl's Fifth Amendment rights were violated because even if they were, the court's decision to admit the evidence was harmless beyond a reasonable doubt. "Statements induced in violation of Miranda's safeguards are appropriate for analysis under the `harmless beyond a reasonable doubt' test." Batista-Polanco, 927 F.2d at 21.
Foss testified that Carl gave his name and said, "Why aren't you arresting the real robbers?" When Foss asked who that was, Carl said, "Bryan and Timothy," and then said that "Bryan was currently in [Carl's] house hiding and that Timothy was at the Sunrise Motel [with Carl's] girlfriend." Carl also said "Timothy had the gun" and "Timothy wouldn't come to [Carl's] home because [Carl] would beat his ass."
Carl's statements to Foss pertain to the robberies, not to drug activity. Carl was convicted of the drug distribution charge but was acquitted of the robbery charges. Because the disputed statements did not provide evidence of drug activity, the statements had little, if any, probative value in proving the drug distribution charge. *122 In addition, as is explained in the context of Carl's Sixth Amendment claim, the government provided substantial evidence of Carl's drug activities through the testimony of Riley, Frisco, and Black, and Foss's testimony about Carl's statements was a minor aspect of the government's case. Therefore, any error in admitting the statements was harmless beyond a reasonable doubt.

C. Drug Quantity

Carl contends that the district court should not have relied on the testimony of Riley, Frisco, and Black to determine the quantity of drugs for sentencing. He argues that the witnesses were inherently unreliable because they were addicted to drugs at the time of the events about which they testified, and because they were motivated to overestimate the amount of drugs Carl distributed to them in order to receive reductions in their own sentences. Carl also suggests that the witnesses' testimony at his sentencing hearing cannot be trusted because it differed from the witnesses' testimony at trial.
On appeal, "we review a sentencing court's factual findings anent drug quantity for clear error." United States v. Platte, 577 F.3d 387, 392 (1st Cir.2009). "Absent a mistake of law . . . we must honor such findings `unless, on the whole of the record, we form a strong, unyielding belief that a mistake has been made.'" Id. (quoting Cumpiano v. Banco Santander P.R., 902 F.2d 148, 152 (1st Cir.1990)).
For its part, the sentencing court must "base [its] findings on reliable information and, where uncertainty reigns, must err on the side of caution." United States v. Sepulveda, 15 F.3d 1161, 1198 (1st Cir.1993) (quotations omitted). A drug quantity determination "need only be supported by a preponderance of the evidence."[4]United States v. González-Vélez, 587 F.3d 494, 502-03 (1st Cir.2009). The court is not required to "be precise to the point of pedantry." Platte, 577 F.3d at 392; see also United States v. Rodriguez, 525 F.3d 85, 107 (1st Cir.2008) (drug quantity determination need only be "a reasoned estimate").
Sentencing courts routinely make determinations about the credibility or reliability of witnesses. "Faced with divergent estimates of drug quantity, a sentencing court is entitled to make judgments about veracity and reliability and to pick and choose among the divergent estimates." Platte, 577 F.3d at 393. Moreover, where, as here, "the sentencing judge. . . preside[s] over the appellant's trial, and . . . see[s] and hear[s] the witnesses. . . he [i]s in an excellent position to gauge their relative credibility." Id.
As in many drug cases, the witnesses here used drugs heavily, have significant criminal histories, and were testifying under the terms of their plea agreements. However, the testimony of each witness at trial was consistent both with what the other witnesses said at trial and with what each said at sentencing. Inconsistencies in the testimony were relatively minor and were explained by the witnesses.
*123 At trial, Riley said that he smoked crack constantly for the two or three weeks leading up to the events of November 6, 2004, and that he always used the proceeds of his criminal deeds to purchase the drugs from Carl. At sentencing, Riley said that Carl provided him with drugs for about three weeks or a month leading up to November 6, and that Carl probably sold him 20 grams or less, in total. Riley noted, however, that he had other dealers and that the days on which he got drugs from Carl would add up to two weeks. At trial, Riley said that he purchased hundred-rocks from Carl, but at sentencing he recalled that Carl was a dishonest businessman and that the hundred-rocks were really only about 0.5 gram each.
At trial and sentencing, Frisco's accounts of Carl giving her drugs beginning on their second date were consistent. Her recollection of taking trips with Carl to purchase drugs, including the number of trips, the destinations, and the amounts of drugs purchased, was also consistent. She testified at sentencing that she got at least 2 grams of crack and 1 gram of powder cocaine from Carl every day from the second week of July through November 6, with the exception of two days when Carl was away and eleven days when she stayed in a shelter.
Similarly, Black's testimony at trial and sentencing that he gave Carl the money from his crimes as well as from his legitimate work was consistent. He testified both at trial and at sentencing that he accompanied Carl three times to buy drugs.
The testimony of Riley, Frisco, and Black would likely have justified both a higher quantity of drugs and a lengthier jail sentence. The district court, however, repeatedly and appropriately exercised caution in each of its determinations regarding the drug quantity. The court used only the amounts that each witness testified he or she received from Carl. Amounts that Carl purchased, including between 5 and 8 ounces from his daughter's boyfriend in Manchester, 1 ounce from the Sanford shopping mall parking lot, and approximately 200 grams from Riverton Park, were not counted. Amounts that Carl sold to other customers, including Riley's mother and her fiancé, were also not included.
In addition, the court used the lowest amounts to which each witness testified. Riley first testified that he bought about 20 grams of crack from Carl. After being walked through a timeline of events, Riley said it was probably more like 0.5 gram per day for two weeks. The court attributed 7 grams to Riley. Frisco testified that she received at least 1 gram of cocaine powder and 2 grams of crack from Carl each day beginning in early July and continuing through November 6, 2004, with the exception of eleven days when she was in a shelter and two days while Carl was away. She also remembered that Carl would sometimes leave her another 1 or 2 grams, or as much as an eight-ball, on top of the regular amount. The court ignored the additional amounts, and found Carl responsible for 106 grams of powder and 212 grams of crack for the 106 days in July through November. Black testified that he bought at least one eight-ballbut sometimes as many as two or three eight-ballseach day in August, September, October, and November 1-6, and that there was one day in October when he bought five or six eight-balls. The court used the lowest number, one eight-ball per day, and attributed 360.5 grams of crack to Black based on ninety-seven days plus six eight-balls on the aberrant day in October.
The court again used caution by sentencing below the guideline range. The amounts that Carl distributed to Riley, *124 Frisco, and Black were equivalent to 11,611.2 kilograms of marijuana. That amount, combined with Carl's criminal history category of I, resulted in a base offense level of 34, which yielded a recommended range of 151-188 months. The court varied downward from the guideline range and sentenced Carl to 120 months in prison. In light of the conservative approach taken by the court in estimating the quantity of drugs for which Carl was held responsible, and the fact that there was adequate support in the record for the court's determination, there was no clear error.

D. Acquitted Conduct

In his brief, Carl argues that the district court erred by failing to resolve a dispute over whether it was proper to include the conduct of which Carl was acquitted in the PSR. He contends that including acquitted conduct in the PSR violated Federal Rule of Criminal Procedure 32(i)(3)(B), which requires, at sentencing, that "the court . . . mustfor any disputed portion of the presentence report or other controverted matterrule on the dispute or determine that a ruling is unnecessary either because the matter will not affect sentencing, or because the court will not consider the matter at sentencing."
During sentencing, Carl objected only to "the use of acquitted conduct for [the court's] consideration" (emphasis added). In response, the district court made a finding that, "[C]ase law permits me to use acquitted conduct. . . . That objection's overruled." It is clear that the court ruled on the asserted objection, and therefore there was no violation of Rule 32(i)(3)(B).
In contrast to what appears in the sentencing transcript, Carl in his brief appears to raise a new theory on appeal. Here, Carl contends that inclusion of the acquitted conduct in his PSR was error because prison personnel may interpret the PSR incorrectly and may improperly classify Carl as a violent felon, based on the acquitted robbery charges. Because Carl's new theory pertaining to the effect of the acquitted conduct on his prison classification was first raised on appeal, it is waived. United States v. Wallace, 573 F.3d 82, 96 n. 13 (1st Cir.2009). Even if that were not the case, his new theory is not sufficiently developed to permit review. United States v. Zannino, 895 F.2d 1, 17 (1st Cir.1990).
Therefore, Carl has not shown that the district court failed to comply with Rule 32(i)(3)(B) or that any other error occurred by including the acquitted conduct in the PSR.

III.
For the foregoing reasons, Carl's conviction and sentence are affirmed.
NOTES
[*]  Of the District of New Hampshire, sitting by designation.
[1]  Riley was the subject of a separate criminal complaint.
[2]  According to the testimonies of Riley, Frisco, and Black, a "hundred-rock" is the amount of crack that can be purchased with one-hundred dollars and is usually approximately 1 gram. Similarly, a "fifty-rock" is the amount of crack that can be purchased for fifty dollars and is usually approximately 0.5 gram. An "eight-ball" is 0.125 ounce, which is approximately 3.5 grams.
[3]  As the government notes, Carl's argument appears to allege violations of both his Sixth and Fifth Amendment rights, although he frames the issue as implicating only the Sixth Amendment. Even if Carl's Fifth Amendment argument were deemed not waived and sufficiently explicated to warrant our review, our analysis would not change. "Statements induced in violation of Miranda's safeguards are appropriate for analysis under the `harmless beyond a reasonable doubt' test." United States v. Batista-Polanco, 927 F.2d 14, 21 (1st Cir.1991).
[4]  Carl asks us to apply a heightened level of scrutiny to the testimony of drug-addicted cooperating witnesses. He asserts that the Third, Sixth, Seventh, and Eighth Circuits have adopted such a standard. See, e.g., United States v. Beler, 20 F.3d 1428, 1435 (7th Cir.1994); United States v. Miele, 989 F.2d 659, 666 (3d Cir.1993); United States v. Simmons, 964 F.2d 763, 776 (8th Cir.1992); United States v. Robison, 904 F.2d 365, 371 (6th Cir.1990). We decline to abandon the standard set forth in Sepulveda and subsequent cases.
