
544 F.3d 743 (2008)
UNITED STATES of America, Plaintiff-Appellee,
v.
Javier HERNANDEZ, Defendant-Appellant.
No. 07-1134.
United States Court of Appeals, Seventh Circuit.
Argued January 14, 2008.
Decided September 12, 2008.
*744 Richard N. Cox (argued), Office of the United States Attorney, Urbana, IL, for Plaintiff-Appellee.
Frederick F. Cohn (argued), Chicago, IL, for Defendant-Appellant.
Before POSNER, KANNE, and WILLIAMS, Circuit Judges.
WILLIAMS, Circuit Judge.
Javier Hernandez pled guilty to conspiring to knowingly distribute cocaine. In the plea agreement, the parties agreed to have the district court determine, beyond a reasonable doubt, the quantity of drugs for which Hernandez would be held accountable in determining his sentence. Because it is unclear how the district court arrived at its drug quantity calculation, we cannot determine whether the government met its burden so we find that the district court committed clear error. We remand this case to the district court to determine the amount of drugs attributable to Hernandez.

I. BACKGROUND
Javier Hernandez was charged with conspiring to knowingly distribute cocaine, in violation of 21 U.S.C. § 841(a)(1). The indictment alleged that more than five kilograms of cocaine and fifty grams of crack were involved in the conspiracy. Pursuant to his plea agreement, Hernandez pled guilty to distributing only one kilogram of cocaine. His plea agreement also stipulated that any further drug quantities had to be proven beyond a reasonable doubt at sentencing. The district court agreed to apply the burden of proof stipulated to by the parties in determining the drug quantity attributable to Hernandez. At the sentencing hearing, Darrell Daily, Melvin Harmon, Troy Powers, and Eric Keith testified that Hernandez provided them with at least 196 kilograms of cocaine over the course of the conspiracy. Daily testified that in September of 2001, Hernandez supplied him with one kilogram of cocaine. Daily then sold this cocaine to Harmon, who sold it to Dumond and Courtney Morris. Hernandez later provided Daily with another kilogram of cocaine after Harmon indicated that the first kilogram was "bad," or unusable. In the remaining months of 2001, Daily continued to sell small amounts of cocaine to the Morrises *745 indirectly through Harmon. Harmon testified that he sold two to three kilograms per month to the Morrises for the remaining months of 2001.
According to the testimony at the hearing, the drug quantities that Daily obtained from Hernandez increased substantially in 2002. In 2002, Hernandez supplied Daily with between one and twelve kilograms of cocaine on multiple occasions, and seventeen kilograms of cocaine on one occasion. Daily supplied Harmon, who sold the Morrises at least six kilograms of cocaine every month in 2002. There were also at least two occasions in 2002 where Daily supplied the Morrises directly with six to seven kilograms of cocaine. By this time, Daily had a supplier other than Hernandez, but it is not clear if Daily began purchasing cocaine from this alternate source in 2002 or 2003.
In 2003, Daily sold approximately twenty-five kilograms of cocaine to Harmon. In late 2003, Hernandez provided Harmon with fifty kilograms of cocaine directly. In 2004, Hernandez continued to supply Harmon, who sold approximately seventy kilograms of cocaine to the Morrises that year. Harmon was arrested in March 2005 for attempting to sell one kilogram of cocaine, which had been provided by Hernandez, to a third party.
Powers testified that in the fall of 2003, he purchased four and a half ounces of cocaine from Hernandez. He also purchased a similar amount of cocaine from Hernandez on two to three other occasions that year. In 2004 and 2005, Powers purchased one to three kilograms of cocaine once or twice a month from Hernandez until Hernandez's arrest in June 2005. Powers estimated that he received fifteen to twenty kilograms of cocaine from Hernandez from early 2004 until June 2005.
Harmon introduced Keith into the drug scheme, and both Harmon and Daily supplied Keith. Keith testified that from 2001 until 2004, he obtained at least one kilogram of cocaine a week from Harmon until Keith's arrest in 2004. In 2002, Daily sold Keith six to seven grams of cocaine, which were provided by Harmon. Keith testified that, by the time of his arrest, he had received seventy kilograms of cocaine from Harmon and five from Daily. All of the cocaine involved in these transactions originated from Hernandez. In 2004, Keith obtained five kilograms of cocaine directly from Hernandez.
Hernandez did not present any witnesses at the hearing, but during cross-examination of the government's witnesses, his attorney elicited testimony indicating that they had made prior inconsistent statements to the agents investigating the case. Hernandez argued that the witnesses were biased because they were receiving benefits from the government in exchange for their testimony, and there were no drug ledgers or other records to corroborate their testimony. In response, the government contended that the witnesses established that Hernandez was responsible for distributing at least 196 kilograms of powder cocaineeight kilograms in 2001; seventy-two kilograms in 2002; twenty-five kilograms in 2003; seventy-five kilograms in 2004; and sixteen kilograms in 2005. The district court ultimately concluded that Hernandez was responsible for distributing 159 kilograms of cocaine, which it considered a "conservative" estimate based on its consideration of the credibility of the witnesses. The court did not explain how it arrived at 159 kilograms, but did indicate that its decision was made beyond a reasonable doubt.
The finding of 159 kilograms resulted in Hernandez having a base offense level of 38. After applying a four-level enhancement for his leadership role in the offense and awarding a two-level reduction for acceptance of responsibility, the court determined *746 that Hernandez had an offense level of 40. With a Criminal History Category of IV, the resulting advisory guidelines range was 360 months to life. The court sentenced Hernandez to 360 months in prison. Hernandez appeals, arguing that there was insufficient evidence to support the district court's sentencing determination regarding drug quantity.

II. ANALYSIS

A. The district court did not commit clear error by crediting the testimony of the government's witnesses at the sentencing hearing.
We review the district court's application of the sentencing guidelines de novo and its factual findings under the clearly erroneous standard of review. United States v. Bennett, 461 F.3d 910, 912 (7th Cir.2006). We will reverse the district court's factual findings only where there is a "definite and firm conviction that a mistake has been committed." Id.; United States v. Noble, 246 F.3d 946, 951 (7th Cir.2001). In determining a drug offender's base offense level, a district court considers quantities of drugs specified in the count of conviction and the quantities that were part of the same course of conduct or common scheme or plan as the offense of conviction. See U.S.S.G. § 1B1.3(a)(2); United States v. Huerta, 239 F.3d 865, 875 (7th Cir.2001). In doing so, "the district court is entitled to estimate drug quantity using testimony about the frequency of dealing and the amount dealt over a specified period of time." Noble, 246 F.3d at 952 (internal citations omitted).
Hernandez disputes the drug quantity determination made by the district court, arguing that the witnesses who testified against him were not credible, and that the government failed to present any evidence to corroborate their testimony, such as ledgers or records memorializing the drug transactions. We have held, however, that "uncorroborated evidence can be a sufficient basis for a sentence." United States v. Johnson, 227 F.3d 807, 813 (7th Cir. 2000). Hernandez's arguments regarding witness credibility are also not persuasive. We are "reluctant to disturb credibility determinations absent a compelling reason," Noble, 246 F.3d at 951, and here, no compelling reason exists. Hernandez focuses most of his efforts on undermining the credibility of Daily and Keith, whose testimony contained gaps and inconsistencies. Hernandez argues that Keith is unreliable because Keith testified that he named Hernandez as his supplier to the agents who arrested Keith, but Hernandez is never mentioned in the agents' reports. Keith eventually told the agents that he had purchased cocaine directly from Hernandez, but it was two years after his initial arrest. This two year gap, Hernandez maintains, destroys Keith's credibility.
The omission of Hernandez from the agents' reports, however, does not necessarily conflict with Keith's later testimony that Hernandez was his supplier. Keith indicated on cross-examination that he did not mention Hernandez because he was not asked about any of his transactions or dealings with Hernandez; additionally, he testified that he had discussed Hernandez on occasions that were not mentioned in the reports. Although Keith does not identify Hernandez as his supplier until two years after his arrest, Keith first mentioned Hernandez to the agents three weeks after Keith's arrest. Keith mentioned to the agents that at one of his transactions with Harmon, he saw someone that he believed to be Harmon's supplier, whom he referred to as "Javy," which is Hernandez's nickname. During this incident, Hernandez brought the cocaine to Harmon, who then sold it to Keith. From this perspective, the district court could have concluded that, despite the time gap, Keith's testimony that he bought five *747 kilograms directly from Hernandez is credible because Keith identified Hernandez as the supplier of the cocaine that he had purchased during his early transactions with Harmon. It would not be a stretch to believe that Keith later obtained cocaine from Hernandez directly.
Hernandez also tried to discredit Harmon's testimony that he received approximately seventy-two kilograms of cocaine indirectly through Hernandez in 2002 because Harmon testified that he never went with Daily to meet Hernandez to pick up the drugs. The fact that Harmon never went with Daily to get drugs from Hernandez does not mean that Hernandez did not supply Daily with the drugs that Harmon received. Harmon testified that "I would inform Darrell Daily that I needed a certain amount ofcertain amount of kilos. . . and then I would meet up with him at his house and I would wait and then Javier would come in and then would leave, then I would have the amount that I was waiting for." From this testimony, there is a strong inference that Hernandez was the source of the drugs that Daily provided to Harmon. In fact, Daily testified that in 2002 he received between one and twelve kilograms of cocaine from Hernandez on multiple occasions and seventeen kilograms on one occasion in particular, and Daily was Harmon's supplier.
Nonetheless, as Hernandez points out, there were inconsistencies in the testimony of the witnesses, particularly Daily. Discrepancies or inconsistent prior statements do not, as a matter of law, render a witness's testimony incredible. United States v. Alcantar, 83 F.3d 185, 189-90 (7th Cir.1996). "In order for testimony to be found incredible as a matter of law, `it must have been either physically impossible for the witness to observe that which he or she claims occurred, or impossible under the laws of nature for the occurrence to have taken place at all.'" United States v. Ortiz, 431 F.3d 1035, 1039 (7th Cir.2005) (citing United States v. McEntire, 153 F.3d 424, 435 (7th Cir. 1998)).
Here the testimony was neither impossible nor improbable, and in fact, the prosecutor tried to account for inconsistencies in the witnesses' testimony by excluding certain amounts where appropriate. For example, Daily gave conflicting testimony about when he started receiving cocaine from a source other than Hernandez, so the government did not rely on Daily's testimony in calculating Hernandez's drug quantity for the year 2003. Additionally, Daily testified that ninety percent of his supply came from Hernandez in 2002, leading the prosecutor to proportionately discount the amount attributed to Hernandez for that year. Also, Harmon initially told authorities that he bought approximately twenty-five kilograms of cocaine directly from Hernandez in 2004, but later testified that he obtained fifty to seventy-five kilograms of cocaine. The prosecutor asked the court to hold Hernandez responsible for only twenty-five kilograms of cocaine, rather than fifty or seventy-five kilograms.
Furthermore, the witnesses' testimonies were fairly consistent with regards to the hierarchy of the drug operation; the business arrangement with the Morrises; and Keith's introduction into the drug scheme. Daily and Harmon corroborated each other's testimony in describing the formation of the drug operation in prison and their initial transaction with the Morrises. They also testified similarly as to the later transactions with the Morrises as well as the introduction of Keith, another of Harmon's former prison mates, into the drug scheme. There was also overlap in testimony regarding the drug quantitiesfor example, Daily testified that in 2001 and 2002, ninety percent of his supply of cocaine came from Hernandez, which was *748 approximately eighty kilograms. Harmon's testimony regarding his distributions to the Morrises was that during those years he sold them approximately eighty kilograms of cocaine, all of which were supplied by Daily. Thus, there is some indicia of reliability to the witnesses' testimony which, when combined with their testimony about the frequency and amount of the drug dealing, could have reasonably led the district court to conclude that much of their testimony was credible. Noble, 246 F.3d at 952 ("The district court is entitled to estimate drug quantity using testimony about the frequency of dealing and the amount dealt over a specified period of time") (citing United States v. Durham, 211 F.3d 437, 444 (7th Cir.2000)).
Finally, Hernandez argues that because Daily, Harmon, and Powers are convicted felons, this fact in and of itself impeaches their credibility. This argument need not detain us long. While this is one factor that the district court can consider in weighing the evidence, it is also within the district court's discretion to give some weight to their testimony, notwithstanding their status as felons. United States v. Johnson, 489 F.3d 794, 797 (7th Cir.2007) (noting that the district court can credit testimony that is "totally uncorroborated and comes from an admitted liar, convicted felon, large scale drug-dealing, paid government informant"). Accordingly, we find that the district court did not commit clear error in finding that the government's witnesses were credible.

B. The district court's drug quantity calculation was clearly erroneous because the district court failed to specify how it determined the amount of drugs attributable to Hernandez.
While the district court could conclude, based on the testimony at the sentencing hearing, that Hernandez conspired to distribute more than 150 kilograms of cocaine, it is unclear how it arrived at the 159 kilograms that it ultimately settled on as the drug quantity amount. The government agrees that, based on the testimony at the sentencing hearing, there is no way to arrive at 159 kilograms as the amount of cocaine attributable to Hernandez. From the record, it is apparent that the district court weighed any perceived conflicts in the testimony, the witnesses' felon status, and the imprecise nature of the drug calculations in reducing Hernandez's drug quantity amount by almost forty kilograms from what the government asked it to consider in imposing sentence. Further, the district court indicated that its estimate was "conservative," suggesting that it believed that Hernandez was responsible for more drugs than it actually attributed to him.
The district court's failure to indicate how it arrived at its drug quantity calculation is problematic, however, because Hernandez's base offense level of 40 corresponds to a drug quantity amount of 150 kilograms or more of cocaine; the court settled on 159 kilograms, which is extremely close to the cutoff of 150 kilograms. See U.S.S.G. § 2D1.1. Had it reduced the drug quantity finding by an additional nine kilograms, the base offense level would have been 36 (the range for 50 to 150 kilograms of cocaine) which, with the four-level enhancement for leadership role in an offense and two-level reduction for acceptance of responsibility, would have been a base offense level of 38. Given Hernandez's Criminal History Category of IV, the advisory guidelines range would be 262-327 months, rather than the range of 360 months to life used by the district court. See U.S.S.G. § 5A.
It is clear that in Hernandez's situation, where the district court's drug quantity *749 calculation placed him on the cusp of a lower guidelines range, every kilogram counts. In particular, Daily's testimony leaves the most room for error. While the government discounted much of Daily's testimony in calculating its drug quantity recommendation, it is not clear what portions of Daily's testimony the district court credited in determining the drug quantity amount attributable to Hernandez. Daily testified that he started buying cocaine from a supplier other than Hernandez in 2002 because of the incident with the "bad kilo," but Daily's proffer statement, which was used to refresh his recollection at the sentencing, indicated that Daily first started buying cocaine from the alternate source in May of 2003. While the government did not include any of Hernandez's sales to Daily in 2003 in its drug quantity calculation because of this discrepancy, it is not clear if the district court also reduced the drug quantity amount for 2002 based on Daily's conflicting testimony that he purchased drugs from an individual other than Hernandez that year.
In addition, Daily initially testified that approximately ninety percent of the cocaine that he sold to the Morrises from 2001 until 2003, either directly or through Harmon, was provided by Hernandez, but later changed his testimony to suggest that the ninety percent figure might not be entirely correct and that Hernandez might not have been Daily's primary source. This testimony suggests that Hernandez's drug sales to Daily may have been less than the amount of drugs that the government sought to attribute to Hernandez from 2001 until 2003.
In contrast, Harmon's testimony indicates that Hernandez might be responsible for more than the drug quantity that the government attributed to Hernandez for the year 2002. For example, Harmon testified that there was at least one instance in 2002 were he provided eight kilograms of cocaine to the Morrises. In calculating drug quantity for 2002, the prosecutor did not include this figure, opting instead to rely on Harmon's testimony that he provided at least six kilograms to the Morrises every month in 2002. The prosecutor also relied on the lower estimate regarding the drugs that Hernandez sold to Harmon in 2004, relying on the figure of twenty-five kilograms because of discrepancies in Harmon's testimony, even though Harmon testified that he was obtaining, on average, ten kilograms a month from Hernandez during that year, and at one point, had obtained eighteen kilograms of cocaine from Hernandez to sell to the Morrises. While the prosecutor's reliance on the lower drug amount is certainly not problematic, these discrepancies illustrate the need for specificity by the district court as to what testimony it relied on in calculating the 159 kilograms it ultimately held Hernandez responsible for, especially given this amount's proximity to the cutoff for the lower base offense level, which corresponds to a drug quantity amount of 50-150 kilograms of cocaine.
We have long recognized that the drug quantity calculation is necessarily imprecise because "drug dealers ordinarily do not use invoices and bills of lading"; therefore, "sentencing courts may make reasonable estimates as to drug quantities." United States v. Rodriguez, 67 F.3d 1312, 1325 (7th Cir.1995). Here, the district court's determination that Hernandez was responsible for 159 kilograms might be a "conservative" estimate given that the government asked it to attribute a drug quantity of 196 kilograms to Hernandez. We also know that the district court did not count eighteen kilograms of cocaine that Hernandez supplied to Powers through a third party after his arrest. Although the district court reduced the drug quantity calculation recommended by the government by almost forty kilograms because of *750 the various contradictions and inconsistencies present in the witnesses' testimony, the district court does not indicate which amounts it actually relied on in calculating the 159 kilograms that it ultimately attributed to Hernandez. Given the various amounts mentioned during the testimony at sentencing and the fact that the district court did not explain how it determined its drug quantity calculation, it is impossible for us to find that there was no error in the calculation.

C. The parties can stipulate to a different burden of proof than that required by law, but we cannot determine from the record if the government met its burden.
In the plea agreement, the parties stipulated that the government has the burden of proving the quantity of drugs attributable to Hernandez beyond a reasonable doubt at sentencing.[1] Usually, the district court makes drug quantity findings at sentencing based on the preponderance standard. United States v. Spiller, 261 F.3d 683, 691 (7th Cir.2001) ("[A]t sentencing, the Government must prove the facts underlying the base offense or an enhancement by a preponderance of the evidence.") (internal citation and quotation omitted). Nevertheless, the district court stated that it made its findings consistent with the standard agreed on by the parties because it assumed it was bound by the stipulation. As a general matter, we do not subscribe to the idea that the court was bound by the parties' stipulation. United States v. Mankiewicz, 122 F.3d 399, 403 n. 1 (7th Cir.1997) ("As the Guidelines themselves make clear, although the plea agreement binds the parties, it does not bind the court."); see also U.S.S.G. § 6B1.4(d) (stating that parties can stipulate to facts relevant to sentencing as a part of a plea agreement, but the court is not obligated to accept the stipulation).
In fact, a district court can reject a plea agreement in its entirety as long as the court "articulates a sound reason for rejecting the agreement." United States v. King, 506 F.3d 532, 535 (7th Cir.2007) (affirming the district court's rejection of a plea agreement on the basis that the sentence within the parties' proposed guidelines range would have been too low to achieve the sentencing goals enumerated in 18 U.S.C. § 3553(a)); see also Fed. R.Crim.P. 11(c)(5) (discussing circumstances in which a district court can reject a plea agreement). This is particularly true here where the parties have stipulated, not to specific facts, but to a different standard for the applicable burden of proof at sentencing. See Swift & Co. v. Hocking Valley R. Co., 243 U.S. 281, 290, 37 S.Ct. 287, 61 L.Ed. 722 (1917) ("the court cannot be controlled by agreement of counsel on a subsidiary question of law"); United States v. One 1978 Bell Jet Ranger Helicopter, 707 F.2d 461, 462 (11th Cir. 1983) ("a stipulation of the parties to an action may be ignored by the court if it is a stipulation as to what the law requires"); King v. United States, 641 F.2d 253, 258 (5th Cir.1981) (same).
However, where a court opts to enforce a plea agreement, it should adhere to the terms agreed upon by the parties. Plea agreements are contracts, and should be interpreted according to principles of contract law. United States v. Randle, 324 F.3d 550, 557-58 (7th Cir. 2003) (citing United States v. Williams, *751 102 F.3d 923, 926-27 (7th Cir.1996)). Like other contracts, plea agreements should be enforced consistent with the intent of the parties and the language of the agreement. United States v. Atkinson, 259 F.3d 648, 654 (7th Cir.2001) ("[W]e review the language of the plea agreement objectively and hold the government to the literal terms of the plea agreement.") (citation omitted).
The district court opted to enforce the stipulation. Initially, we note that there does not appear to be any harm from its decision to do so.[2] Unlike a situation in which a defendant has waived one of his rights as a part of a constitutionally impermissible plea agreement, or where the parties have stipulated to some unorthodox practice, the same concerns are not present here. See United States v. Hicks, 129 F.3d 376, 377 (7th Cir.1997) ("a sentence based on constitutionally impermissible criteria, such as race, is invalid even though the defendant executed a blanket waiver of his rights"); United States v. Feichtinger, 105 F.3d 1188, 1190 (7th Cir. 1997) (a sentence in excess of the statutory maximum sentence for the defendant's crime invalidates sentence, notwithstanding defendant's stipulation waiving his right to appeal); United States v. Andrews, 895 F.2d 406, 409 (7th Cir.1990) (where the defendant waived his right to have a trial declared a mistrial after extrinsic evidence was submitted to the jury, "what is important to our inquiry is that the trial court's acceptance of this waiver was not so offensive to our concept of ordered liberty so as to shock our conscience"); United States v. Josefik, 753 F.2d 585, 588 (7th Cir. 1985) (finding that limitations exist on the ability of parties to stipulate to the structure of the jury at trial because "if the parties stipulated to trial by 12 orangutans the defendant's conviction would be invalid notwithstanding his consent, because some minimum of civilized procedure is required by community feeling regardless of what the defendant wants or is willing to accept.").
Most notably, none of the defendant's constitutional rights are infringed by the stipulation and the standard chosen by the parties is one with which the district court is familiar. Furthermore, the sentencing hearing was conducted in a manner that did not substantially deviate from statutory or constitutional norms, and neither party has contested the stipulation on appeal. Had any of these factors not been present, the stipulation might be invalid.
The problem is that we cannot determine if the district court calculated the amounts of drugs attributable to Hernandez using the reasonable doubt standard. The court did not explain how it arrived at 159 kilograms as the drug quantity amount; thus, it is not clear from the record if the district court acted in accordance with the stipulation, as it purported to do.

III. CONCLUSION
Accordingly, we REVERSE and REMAND this case for proceedings consistent with this opinion.
NOTES
[1]  The defendant also argues that the district court should have adhered to the Federal Rules of Evidence at his sentencing hearing because the parties agreed to a higher burden of proof. The defendant offers no authority for this position and the parties did not explicitly agree to such an arrangement. Therefore, we will not read new terms into the plea agreement.
[2]  Although neither side challenges the validity of the stipulation, where the parties have changed the burden of proof through their plea agreement, it is within the realm of our authority to question, sua sponte, the propriety of doing so. See Kamen v. Kemper Fin. Servs., 500 U.S. 90, 99, 111 S.Ct. 1711, 114 L.Ed.2d 152 (1991) ("When an issue or claim is properly before the court, the court is not limited to the particular legal theories advanced by the parties, but rather retains the independent power to identify and apply the proper construction of governing law.")
