
643 F.3d 545 (2011)
UNITED STATES of America, Plaintiff-Appellee,
v.
Willie Earl JOHNSON, Defendant-Appellant.
No. 10-2503.
United States Court of Appeals, Seventh Circuit.
Argued February 16, 2011.
Decided June 28, 2011.
*548 Matthew M. Getter (argued), Attorney, Office of the United States Attorney, Chicago, IL, for Plaintiff-Appellee.
Thomas R. Mikrut, Attorney, Foley & Lardner, LLP, Chicago, IL, Brian H. Potts (argued), Attorney, Foley & Lardner LLP, Madison, WI, for Defendant-Appellant.
Before POSNER, FLAUM, and SYKES, Circuit Judges.
FLAUM, Circuit Judge.
This panel vacated Willie Earl Johnson's conviction for conspiring to distribute drugs and remanded to the district court to resentence him on his two remaining convictions. See United States v. Johnson, 592 F.3d 749 (7th Cir.2010). After resentencing, Johnson appeals again, this time arguing that the district court committed procedural errors at resentencing and erred in reaching its relevant conduct finding. With some reluctance, we affirm the relevant conduct finding. But we remand because the district court did not respond to Johnson's repeated requests for a reduced crack-to-powder ratio.

I. Background
Johnson and eight other defendants were indicted on charges related to selling crack cocaine and heroin in and around Aurora, Illinois, from approximately 2002 until 2005. Johnson was charged with conspiring to distribute and to possess with intent to distribute controlled substances in violation of 21 U.S.C. §§ 841(a)(1) and 846 (Count One), possessing with intent to distribute a controlled substance, in violation of 21 U.S.C. § 841(a)(1) (Count Eleven), and utilizing a telephone to facilitate a felony drug crime, in violation of 21 U.S.C. § 843(b) (Count Twelve). Seven Defendants pled guilty, while Johnson and his co-defendant Ismael Garza went to trial.
A jury found Johnson guilty on all three counts and concluded in a special verdict that he was accountable for between five and fifty grams of crack. At his first sentencing hearing, the district court attributed 31.5 grams of crack to him and sentenced him to 72 months' imprisonment on Counts One and Eleven, and 48 months' imprisonment on Count Twelve, to run concurrently.
On appeal, we vacated Johnson's conviction on Count One due to insufficient evidence, but affirmed his remaining convictions on Counts Eleven and Twelve. Johnson, 592 F.3d at 759. Accordingly, we remanded for resentencing on Counts Eleven and Twelve because the jury's special verdict assigning a quantity of five to fifty grams of crack was vacated with the conspiracy count. Id.
On remand, at Johnson's second sentencing hearing, the parties disputed whether phone calls between Johnson and Craig Venson, the kingpin of drug conspiracy, supported a relevant conduct finding under United States Sentencing Guidelines ("U.S.S.G.") § 1B1.3 based on drug transactions discussed in the calls, and, if so, the quantities and types of drugs for which Johnson was responsible. Johnson also requested a 1:1 crack-to-powder ratio, instead of 100:1.
The district court found by a preponderance of the evidence that Johnson was accountable for 23 grams of crack and calculated a guidelines range of 92 to 115 months. After considering the factors in § 3553(a), the district court sentenced him to 72 months' imprisonment on Count *549 Eleven and 48 months' imprisonment on Count Twelve, to be served concurrently.

II. Analysis

A. The Crack/Powder Disparity at Sentencing
Johnson argues that the district court committed a procedural error at resentencing by not expressly responding to his repeated requests for a 1:1 crack-to-powder ratio. We review de novo whether the district court followed proper sentencing procedures. United States v. Coopman, 602 F.3d 814, 817 (7th Cir.2010).
We agree with Johnson that the district court erred. A sentencing court need not respond expressly to every argument a defendant makes, but it must address "`all of a defendant's principal arguments that are not so weak as to not merit discussion.'" United States v. Arberry, 612 F.3d 898, 899 (7th Cir.2010) (quoting United States v. Villegas-Miranda, 579 F.3d 798, 801 (7th Cir.2009)). At resentencing, the district court briefly discussed some of the factors in § 3553(a). But it never responded to Johnson's repeated requests for a reduced ratio. Johnson specifically referenced the district court's authority "to reject and vary categorically from the crack-cocaine Guidelines based on a policy disagreement with those Guidelines," Spears v. United States, 555 U.S. 261, 129 S.Ct. 840, 844, 172 L.Ed.2d 596 (2009), listed policy grounds that have motivated other sentencing courts to apply a reduced crack-to-powder ratio, and asked multiple times for a reduced ratio. His argument for a reduced ratio was one of his primary contentions at resentencing and was certainly not so weak as to not merit discussion. See id. at 843-44; Kimbrough v. United States, 552 U.S. 85, 91, 110, 128 S.Ct. 558, 169 L.Ed.2d 481 (2007); Arberry, 612 F.3d at 899-901. In fact, numerous other judges in the Northern District of Illinois have applied lower ratios. See, e.g., United States v. Edwards, No. 04-cr-1090-5, slip op. at 6, 2009 WL 424464, at *3 (N.D.Ill. Feb. 17, 2009) (Gottschall, J.) (concluding "that a 10:1 ratio is all that can possibly be justified" in light of "evidence that the harms produced by powder and crack are essentially the same (with the unquantifiable possibility that crack may be more addictive)"); United States v. Rodriguez, No. 08-cr-509-1, slip op. at 4-5, 2009 WL 1811001, at *2 (N.D.Ill. June 23, 2009) (Darrah, J.) (applying a 20:1 ratio).
Our holding in United States v. Arberry, 612 F.3d 898 (7th Cir.2010), is directly on point. In that case, we vacated a defendant's sentence and remanded for resentencing because the district court did not respond to the defendant's argument for a 1:1 ratio, which was one of his principal arguments at sentencing. Id. at 900-01.
We disagree with the government's contention that Arberry is meaningfully distinct because the defendant in that case received a within-guideline sentence, albeit on the low end of the applicable guideline range, and Johnson received a below-guideline sentence. Id. at 899. Arberry applies because the district court there, as here, did not respond to a criminal defendant's principal, plausible argument for a reduced crack-to-powder ratio. The government points out that we wrote in United States v. Poetz, 582 F.3d 835 (7th Cir. 2009), that the "requirement that the district court specifically address the defendant's principal, potentially meritorious sentencing arguments applies with less force" where "the judge received voluminous evidence and listened carefully to [the defendant's] arguments ... and in the end imposed a short prison sentence significantly below the applicable guidelines range." Id. at 837. Arberry's force may be weakened, but it still applies.
*550 We also reject the government's argument that the district court implicitly addressed Johnson's request for a lower ratio. See, e.g., United States v. Carrillo-Esparza, 590 F.3d 538, 540 (7th Cir.2010); Poetz, 582 F.3d at 837-40. The government directs us to Poetz, which we find distinct because the record in that case demonstrated that the district court considered the defendant's arguments about her and her family's medical problems and the impact of incarceration as opposed to home confinement on her family, even though it did not expressly address each argument on the record. 582 F.3d at 837-40. Specifically, we explained that "Poetz's health problems took center stage" during sentencing, and "the judge imposed a sentence substantially below the applicable guidelines range largely because of her medical condition." Id. at 838. We also found that the district court implicitly expressed that it believed imprisonment, as opposed to home confinement, was necessary based on a portion of the record where "[t]he judge explained that despite Poetz's medical issues, a period of incarceration was `fundamentally required' to promote respect for the law, provide for deterrence, and hold Poetz accountable for her breach of the trust placed in stewards of public funds." Id. We concluded that "`anyone acquainted with the facts would have known without being told why the judge had not accepted the argument.'" Id. (quoting United States v. Cunningham, 429 F.3d 673, 679 (7th Cir.2005)). Finally, we explained that Poetz's argument about the effect of incarceration on her family lacked legal support and, regardless, we found that the district court implicitly considered her argument based on the fact that the judge had voluminous evidence before him substantiating the argument and "[his] sentencing remarks [we]re peppered with references to [Poetz's] family." Id. at 839.
Unlike in Poetz, the record provides no indication that the district court implicitly considered Johnson's argument for a reduced ratio. Although Johnson received a below-guideline sentence, we have no basis to conclude that his sentence had anything to do with the crack/powder disparity. To the contrary, it appears that the district court calculated Johnson's guideline range based on a 100:1 ratio and showed no receptiveness to his argument for a reduced ratio. We have no grounds to conclude that the district court applied a reduced ratio, as opposed to setting a below-guideline sentence based on a 100:1 ratio, or that the district court's decision to impose a below-guideline sentence was in any way related to the crack/powder disparity. We cannot assume that the district court implicitly considered Johnson's argument for a reduced ratio merely because it imposed a below-guideline sentence. Rather, we assume only that if the district court had applied a reduced ratio or decided to impose a below-guideline sentence based on the crack/powder disparity, it would have expressly or implicitly indicated as much on the record.
Accordingly, we vacate Johnson's sentence and remand to give the district court an opportunity to consider and address his arguments for a reduced crack-to-powder ratio. The district court need not conduct a complete sentencing hearing, although, as we explain below, we invite it to do so.
We reject Johnson's request for a broader remedy. Relying on Spears v. United States, 555 U.S. 261, 129 S.Ct. 840, 172 L.Ed.2d 596 (2009), he asks us to categorically prohibit the district courts in the Northern District of Illinois from using the 100:1 ratio based on policy considerations indicating the disparity's unfairness. But Spears does not authorize us to grant such relief. The Court in Spears *551 wrote merely that "district courts are entitled to reject and vary categorically from the crack-cocaine Guidelines based on a policy disagreement with those Guidelines." Id. at 843-44 (emphasis added); see also United States v. Corner, 598 F.3d 411, 414-15 (7th Cir.2010). That authority resides in district courts, not courts of appeals. See Spears, 129 S.Ct. at 843-44; Kimbrough, 552 U.S. at 91, 110, 128 S.Ct. 558; see also Corner, 598 F.3d at 415 ("We understand Kimbrough and Spears to mean that district judges are at liberty to reject any Guideline on policy groundsthough they must act reasonably when using that power."). The courts of appeals review sentences for procedural errors and substantive reasonableness, see, e.g., Gall v. United States, 552 U.S. 38, 51, 128 S.Ct. 586, 169 L.Ed.2d 445 (2007); United States v. West, 628 F.3d 425, 431 (7th Cir.2010), but we cannot categorically prohibit all sentencing courts from applying a 100:1 ratio.
We thus reject Johnson's final argument related to the crack/powder disparity, that his sentence is unreasonable based on the fact that the district court did not apply a reduced ratio. As explained above, the district court had discretion to apply a 100:1 ratio and to impose a below-guideline sentence. We find no abuse of discretion.

B. Relevant Conduct
In Johnson's first appeal, we vacated his conspiracy conviction but found that the intercepted phone calls on July 2, 2004, supported his conviction for possessing crack with intent to distribute, in violation of 21 U.S.C. § 841(a)(1). Johnson, 592 F.3d at 757-59. Based on those calls, the district court determined at re-sentencing that Johnson possessed with intent to distribute 3.5 grams of crack on July 2, and ultimately attributed 23 grams of crack to him in setting his sentence based on the intercepted calls between Johnson and Venson that evidenced crack transactions between the two.
"A court may increase a defendant's sentence for uncharged and unconvicted relevant conduct provided that the conduct constitutes part of the `same course of conduct or common scheme or plan as the offense of conviction.'" United States v. Stephenson, 557 F.3d 449, 456 (7th Cir.2009) (quoting U.S.S.G. § 1B1.3(a)(2)); see also United States v. Singleton, 548 F.3d 589, 591-92 (7th Cir. 2008). "Conduct that qualifies as relevant is factored into the Guidelines' sentencing calculations as if the defendant had been convicted of that conduct, even though the defendant was neither charged nor convicted of the additional crime or crimes." United States v. White, 519 F.3d 342, 347 (7th Cir.2008). The government bears the burden of establishing relevant conduct by a preponderance of the evidence. Id. at 347; United States v. Acosta, 85 F.3d 275, 279 (7th Cir.1996). As long as the district court based its conclusion on reliable information, we review its determination that relevant conduct occurred and its calculation of the drug amount attributable to the defendant for clear error. See White, 519 F.3d at 348; Acosta, 85 F.3d at 279. We reverse "only if, after reviewing the entire record, we are left with the firm and definite conviction that a mistake has been made." United States v. Cross, 430 F.3d 406, 410 (7th Cir.2005) (internal quotation marks and citation omitted).
The district court relied on intercepted phone calls between Johnson and Venson on July 1, 2, and 6, and August 14, 20, and 31, among other evidence, to hold Johnson accountable for 23 grams of crack in setting his sentence. It concluded that each call evidenced occasions on which Johnson purchased drugs and either resold them or *552 intended to, and thus that each constituted relevant conduct under U.S.S.G. § 1B1.3.
Johnson contends that the district court committed four errors in reaching its drug quantity finding: (1) it clearly erred by finding that he possessed and sold or intended to sell the crack discussed in the intercepted calls, and that the code words "pack," "basketball," and "quarter pounder with cheese" referred to 1 gram, 3.5 grams, and 7 grams of crack, respectively; (2) it improperly based its relevant conduct finding on testimony from unreliable witnesses; (3) it did not explicitly find that his unconvicted conduct was sufficiently related to the convicted offense to constitute relevant conduct; and (4) it should not have considered FBI Special Agent Thomas Wilson's testimony at resentencing. While acknowledging that this is a close case, we conclude that the district court did not clearly err in attributing 23 grams of crack to Johnson, and we reject his remaining arguments.

1. The District Court's Relevant Conduct Finding
First, the district court did not clearly err in concluding that Johnson possessed and sold or intended to sell the crack discussed in the intercepted calls on July 1, 2, and 6, and August 14, 20 and 31. Johnson concedes that there is sufficient evidence for the district court to have found that he possessed with intent to distribute the 3.5 grams of crack discussed in the July 2 calls, which formed the basis of his conviction. There is also record evidence indicating that he met Venson on August 14 shortly after requesting crack from him on an intercepted call, and that he intended to resell the drugs shortly after Venson delivered them. Johnson correctly points out that there is less evidence that he possessed and distributed or intended to distribute the drugs he ordered on the other calls. But after reviewing the record, we are not "left with the firm and definite conviction that a mistake has been made." Cross, 430 F.3d at 410 (internal quotation marks and citation omitted).
We similarly find no clear error in the district court's decision that a "pack" referred to 1 gram of crack, a "basketball" 3.5 grams of crack, and a "quarter pounder with cheese" 7 grams of crack. While the intercepted calls between Johnson and Venson do not indicate the quantities of drugs to which the code words they used refer, other record evidence, including testimony from Tosumbua Parker, one of Johnson's co-defendants, and a concession by Johnson's trial counsel, supports the district court's conclusion.
Despite our conclusion that there is enough evidence to affirm the district court's relevant conduct finding, however, Johnson correctly points out that we must reverse if the evidence was not sufficiently reliable. See United States v. Wilson, 502 F.3d 718, 721-22 (7th Cir.2007); Acosta, 85 F.3d at 281-82. He specifically contends that Parker, Agent Michael Culloton, and Agent Wilson provided unreliable testimony. While they could have provided stronger testimony, after reviewing the record, we find sufficient indicia of reliability that their relevant testimony was likely accurate.

2. Explicit Findings
We also disagree with Johnson's argument that the district court erred by not explicitly finding that the transactions on July 1 and 6, and August 14, 20, and 31 were sufficiently related to the offense of conviction, which occurred on July 2, to constitute relevant conduct. See U.S.S.G. § 1B1.3. See generally United States v. Arroyo, 406 F.3d 881, 889 (7th Cir.2005) ("When a district court aggregates drug *553 quantities arising from uncharged or unconvicted relevant conduct for purposes of calculating a defendant's base offense level, we have required the court to explicitly state and support, either at the sentencing hearing or (preferably) in a written statement of reasons, its finding that the unconvicted activities bore the necessary relation to the convicted offense." (internal quotation marks and citations omitted)); United States v. Winbush, 580 F.3d 503, 513-14 (7th Cir.2009). First, although the district court did not expressly use the phrases "same course of conduct" or "common scheme," which appear in U.S.S.G. § 1B1.3, the record demonstrates that it made the necessary findings. See Wilson, 502 F.3d at 723 (upholding a finding under U.S.S.G. § 1B1.3 where, although the court did not specifically use the phrases in the sentencing guidelines, it was clear from the record that the court made the requisite findings); see also United States v. Williams, 272 F.3d 845, 852 (7th Cir. 2001); Acosta, 85 F.3d at 280. Regardless, Johnson concedes in his reply brief, and we agree, that "[i]f the Government had introduced sufficient evidence to prove by a preponderance of the evidence that Johnson possessed and distributed (or intended to distribute) the drugs involved in calls [on days other than July 2], then those transactions would be relevant because they were temporally related and involved transactions with the same group of sellers." Thus, since we conclude that the government did introduce sufficient evidence, even if the district court erred, the error was harmless. See FED.R.CRIM.P. 52(a); Arroyo, 406 F.3d at 890 (no plain error where the district court assumed without specifically finding that the defendant's cocaine activity was sufficiently related to his heroin conviction because "the record could support the conclusion that the two offenses were part of the same course of conduct").

3. Agent Wilson's Testimony at Resentencing
Finally, we find no merit to Johnson's claim that the district court erred by considering Agent Wilson's testimony at resentencing. The district court initially sustained Johnson's objection to Agent Wilson testifying, finding his testimony tentative and imprecise and concluding that the government had not shown enough to present him as a witness. But after the government presented a Report to Congress discussing the prices of crack based on data from twenty American cities and relied on it to make arguments about the price of crack in Aurora, the government asked that Agent Wilson be allowed to testify about drug prices, since his experience included investigations in Aurora, the Chicago area, and Washington, D.C. The district court ultimately permitted Agent Wilson to testify, and he proceeded to discuss crack prices, use and distribution quantities of crack, and various code words drug dealers use. Johnson claims that the district court erred by permitting Agent Wilson to testify, and references the fact that the district court did not specify whether Agent Wilson was testifying as an expert.
First, Johnson's argument is waived because he provides no authority indicating that the district court erred by permitting Johnson to testify. See United States v. Useni, 516 F.3d 634, 658 (7th Cir.2008) (failure to cite relevant authority constitutes waiver). But even if not waived, his argument is meritless.
The Federal Rules of Evidence do not apply in sentencing hearings and the district court was entitled to rely on [a witness]'s testimony even if it may not have qualified as expert testimony under Federal Rule of Evidence 702. The Guidelines (and the Due Process Clause) *554 allow sentencing courts to rely on information that `has sufficient indicia of reliability to support its probable accuracy.'
United States v. Hunter, 145 F.3d 946, 952 (7th Cir.1998) (quoting U.S.S.G. § 6A1.3(a)); see also United States v. Schroeder, 536 F.3d 746, 752 (7th Cir. 2008). As explained above, Agent Wilson's testimony was sufficiently reliable to permit its consideration at sentencing. The district court did not err by considering it.

III. Conclusion
For the foregoing reasons, we VACATE Johnson's sentence and REMAND for the district court to consider his argument for a reduced crack-to-powder ratio. We AFFIRM the district court's decision to attribute 23 grams of crack to Johnson. But we note that the evidence appears to have permitted a lower drug quantity finding. Although our standard of review on appeal prevents us from directing the district court to re-open fact finding on this issue, the interests of justice may warrant reconsideration of Johnson's relevant conduct, and we invite the district court to do so.
