*756Anthony Rowe was charged in a one-count indictment with distribution and possession with intent to distribute 1000 grams of heroin in violation of 21 U.S.C. § 841(a)(1) and (b)(1)(A). Rowe conceded that he distributed approximately 200 grams, so the trial focused on whether he had actually distributed 1000 grams or more. The jury returned a general verdict finding Rowe guilty of the offense in the amounts of both 1000 grams or more and 100 grams or more. Rowe argues that the evidence was insufficient to convict because the Government did not prove that he distributed or possessed 1000 grams of heroin in a single unit, instead relying on evidence of multiple smaller distributions and possessions during the indictment period. He also challenges his sentence, arguing that the District Court relied on information lacking sufficient indicia of reliability to determine his offense level.
We agree that the evidence was insufficient to support the 1000-gram verdict. We will therefore vacate the judgment of conviction based on the 1000-gram verdict and remand to the District Court to enter a judgment of conviction based on the 100-gram verdict. Because this conclusion resolves Rowe's appeal of the judgment, we will not address his additional arguments concerning duplicity of the indictment and prosecutorial misconduct. Regarding Rowe's sentence, we will vacate and remand for re-sentencing with the instruction that the Government may not introduce additional evidence on drug quantity.
I.
A. Investigation, Arrest, and Indictment
Government witness and confidential informant William Pierce was arrested on April 20, 2016 after about ten grams of marijuana and forty grams of heroin were discovered in the rental car he was driving. Pierce offered to cooperate and subsequently made controlled transactions under surveillance. On June 25, 2016, Pierce paid Rowe $ 3900 and received 198.86 grams of heroin, and on June 27, 2016, Pierce paid him $ 7000 in pre-recorded bills for heroin Pierce had previously received. Rowe was arrested shortly afterward. Officers recovered a small notebook, several cell phones, and cash that matched the pre-recorded bills.
Rowe was indicted in the Middle District of Pennsylvania for one count of distributing and possessing with intent to distribute 1000 grams and more of heroin, a Schedule I controlled substance, from on or about February 2016 through on or about June 25, 2016, in violation of 21 U.S.C. § 841(a)(1) and (b)(1)(A).
B. The Trial
At trial, Rowe conceded that he had delivered approximately 200 grams of heroin to Pierce while under surveillance. Due to Rowe's concession, the only contested issue was drug weight; the jury was charged with determining whether Rowe *757distributed or possessed with intent to distribute 1000 grams or more of heroin, or a lesser amount (100 grams or more). The Government's theory throughout the trial was that because Rowe distributed or possessed with intent to distribute a total of 1000 grams or more of heroin during the indictment period, a 1000-gram verdict was justified. To support its theory, the Government presented the testimony of Pierce and a Drug Enforcement Administration agent, as well as the notebook found when Rowe was arrested.
1. Testimony of Confidential Informant William Pierce
Pierce's testimony implicated Rowe in sales totaling as much as 1700 grams of heroin during the indictment period. Pierce testified that when he met Rowe for the first time in February 2016, he attempted to purchase twenty-eight grams of heroin, but actually received twenty-one grams (a discrepancy that Rowe attributed to unintentional error). During this first meeting, Pierce saw a black bag (which he described as a "regular ... little store bag") in Rowe's vehicle with six to eight packages inside, with numbers on each package that read "50 or a hundred or 75." App. 169a. Pierce believed these numbers indicated the amount of drugs in the packages.
In the following months, Pierce testified that he bought heroin from Rowe one to two times a week for $ 75 to $ 85 per gram. Pierce recalled buying twenty-one grams in February 2016 and fifty grams shortly thereafter. There were larger transactions as well: eight purchases of 100 grams and three purchases of 150 to 200 grams. Pierce also testified about the two controlled transactions.1 Pierce testified that in all, he bought $ 80,000 to $ 140,000 worth of heroin from Rowe at around $ 82.50 per gram, which would indicate a total amount of 969.7 to 1697 grams.
Pierce testified that Rowe often wrote in "little notebooks." App. 209a-210a. When presented with the notebook confiscated from Rowe upon his arrest, Pierce testified that notations on a page marked "DO" tracked his purchase and payment history with Rowe, including the controlled transactions.
2. Expert Testimony of DEA Special Agent Shuffelbottom
DEA Special Agent Eric Shuffelbottom, who had experience in narcotics, undercover investigations, and domestic and international drug smuggling, provided expert testimony. He testified that based on his experience, the notebook appeared to be a drug ledger, that is, "a record keeping of drug transactions and money transactions." App. 363a. He testified that the initials at the tops of the pages likely referred to customers, and that the numbers below the initials likely referred to the amount of product fronted to each customer. Special Agent Shuffelbottom further testified that additional notations tracked customers' payments and remaining debts. He explained that the notation "275x70" on the inside cover of the ledger could refer to a 275-gram purchase of a $ 70-per-gram substance.
In addition to testifying about the ledger, Special Agent Shuffelbottom testified generally about the heroin trade. For example, he testified that one thousand grams of heroin could cost between $ 65,000 and $ 75,000 and that individual amounts of heroin were often packaged in "thin wax paper bags." App. 358a. Special *758Agent Shuffelbottom also testified that a dealer selling 200 grams of heroin at a time would likely have access to multi-kilogram quantities. Finally, he testified about how dealers use cell phones to conduct business and that they often transport drugs from larger cities to smaller communities by car.
3. The Ledger
The Government argued that the notebook was Rowe's drug ledger, pointing to Pierce's and Special Agent Shuffelbottom's testimony, and also drawing connections between Pierce's testimony, the notations on the "DO" page, and the marked funds from the controlled transactions. Over defense counsel's objection, the District Court admitted the ledger in its entirety.
4. Closing Argument
In closing, the prosecutor argued, based on the evidence of multiple distributions, that the Government presented sufficient evidence to prove the 1000-gram drug weight. For instance, he tallied the figures in the ledger to arrive at a "drug ledger total" of 1066 grams. App. 405a. He argued that Pierce's testimony and his corresponding page in the ledger indicated that the notations in the ledger referred to heroin.
5. The Instructions, Verdict, and Post-Trial Motion
The District Court instructed the jury that it had to decide "whether the Government has proved beyond a reasonable doubt that Mr. Rowe distributed 1 kilogram or more of heroin." App. 452a. The jury also had the option of returning a verdict for the lesser-included 100 grams. It returned a guilty verdict for both drug weights.
Rowe filed a post-trial motion for a judgment of acquittal or a new trial, arguing that the evidence was insufficient to support the jury's 1000-gram verdict, particularly because the District Court did not instruct the jury on how to "determine the particular weight of heroin that was involved in the crime." App. 496a. The District Court denied the motion.
C. Sentencing
Rowe objected to the Presentence Report (PSR) calculation that his offense involved at least ten kilograms of heroin, resulting in a base offense level of thirty-four under U.S.S.G. § 2D1.1(c)(3). The PSR determination was based on a statement Rowe was alleged to have made at the time of his arrest regarding his heroin supplier. However, evidence of that statement had been excluded at trial, and the Government neither called a witness nor introduced any documentary evidence concerning the statement at sentencing. Rowe therefore argued that the Government had not presented any evidence that his offense involved the requisite ten kilograms of heroin. Despite Rowe's objection, the Court "adopt[ed] the pre-sentence investigation report without change," App. 549a, and imposed a within-Guidelines sentence of 151 months' imprisonment followed by five years' supervised release.
II.2
A. Insufficient Evidence to Support the 1000-Gram Verdict
Our review of the sufficiency of the evidence is plenary, but "we must consider the evidence in the light most favorable to the government and affirm the judgment if there is substantial evidence *759from which any rational trier of fact could find guilt beyond a reasonable doubt." United States v. Benjamin , 711 F.3d 371, 376 (3d Cir. 2013) (citations and internal quotation marks omitted). Our task therefore is to determine "whether the Government has adduced sufficient evidence respecting each element of the offense charged to permit jury consideration." United States v. Miller , 527 F.3d 54, 63 (3d Cir. 2008) (citation omitted).
The Government may rely on direct and circumstantial evidence to make its case to the jury. United States v. Caraballo-Rodriguez , 726 F.3d 418, 425 (3d Cir. 2013). While it is axiomatic that reasonable inferences can support a verdict, they "must bear a logical or convincing connection to established fact." Id. (citation and internal quotation marks omitted). In the end, "[t]he question is whether all the pieces of evidence against the defendant, taken together, make a strong enough case to let a jury find [the defendant] guilty beyond a reasonable doubt." Id. at 432 (quoting United States v. Cooper , 567 F.2d 252, 254 (3d Cir. 1977) ).
The Government charged Rowe with violating 21 U.S.C. § 841(a)(1) by two means: distributing heroin, and possessing it with intent to distribute. The Government further charged that the violation involved 1000 grams or more of heroin, but provided the jury with two options for a finding on drug weight: 1000 grams or more, and 100 grams or more. Under § 841(b)(1)(A)(i), a violation of § 841(a) involving 1000 grams or more of heroin requires a mandatory minimum penalty of ten years' imprisonment and sets a maximum penalty of life imprisonment. Under § 841(b)(1)(B)(i), a violation of § 841(a) involving 100 grams or more of heroin requires a mandatory minimum penalty of five years' imprisonment and sets a maximum penalty of forty years' imprisonment. Because the weight involved in a violation of § 841(a) increases the statutory penalty, it is an element of the offense that must be proven beyond a reasonable doubt. See Alleyne v. United States , 570 U.S. 99, 103, 133 S.Ct. 2151, 186 L.Ed.2d 314 (2013) ("Any fact that, by law, increases the penalty for a crime is an 'element' that must be submitted to the jury and found beyond a reasonable doubt."). Therefore, the question presented here is whether the evidence was sufficient to allow a jury to find that Rowe violated § 841(a) by distributing 1000 or more grams of heroin, or by possessing with intent to distribute 1000 or more grams of heroin.
Under 21 U.S.C. § 802(11), distribution occurs when a controlled substance is delivered. Delivery is "the actual, constructive, or attempted transfer of a controlled substance." 21 U.S.C. § 802(8). Our sister circuits have held that "[t]he plain language of [ § 841(a) ] indicates" that "each unlawful transfer [is] a distinct offense." United States v. Lartey , 716 F.2d 955, 967 (2d Cir. 1983). See United States v. Mancuso , 718 F.3d 780, 793 (9th Cir. 2013) ; see also United States v. Elliott , 849 F.2d 886, 889 (4th Cir. 1988) ("The more precise terms 'deliver' and 'transfer' suggest that Congress intended the statute to criminalize individual acts, rather than a continuous course of conduct."). We agree with their reasoning and hold that "separate acts of distribution of controlled substances are distinct offenses under 21 U.S.C. § 841(a), as opposed to a continuing crime." Mancuso , 718 F.3d at 793.3
*760At trial, the Government did not present evidence of a single distribution involving 1000 grams or more of heroin. The prosecutor mistakenly believed that distribution of 1000 grams could be proven by combining several distributions that, in total, involved 1000 grams of heroin. Rowe challenged this approach in his post-trial motion. The District Court confirmed that the Government was mistaken, and the Government concedes the same before this Court.4 However, the District Court found that because Rowe was also charged with possession with intent to distribute, a continuing offense, the jury's general verdict could stand. We disagree. As we will now explain, the Government's understanding of possession with intent to distribute was also flawed, and the Government did not present sufficient evidence of possession with intent to distribute 1000 grams of heroin.
Possession with intent to distribute is actual or constructive possession over a controlled substance, United States v. Crippen , 459 F.2d 1387, 1388 (3d Cir. 1972) (per curiam), by a defendant who "ha[s] in mind or plan[s] in some way" to "deliver or transfer possession or control" of the controlled substance to another. Third Circuit Model Criminal Jury Instruction § 6.21.841-5. Constructive possession requires "the power and the intention at a given time to exercise dominion or control over a thing." Benjamin , 711 F.3d at 376 (quoting United States v. Garth , 188 F.3d 99, 112 (3d Cir. 1999) ). Proof that a defendant associated with a person who controls a drug is insufficient to prove constructive possession. Garth , 188 F.3d at 112.
Unlike distribution, possession with intent to distribute is a continuing offense. United States v. Zidell , 323 F.3d 412, 422 (6th Cir. 2003) (collecting cases).5 "A continuing offense is a continuous, unlawful act or series of acts set on foot by a single impulse and operated by an unintermittent force, however long a time it may occupy." United States v. Midstate Horticultural Co. , 306 U.S. 161, 166, 59 S.Ct. 412, 83 L.Ed. 563 (1939) (citation omitted). In Benjamin , we looked at another possession statute-felon in possession of a firearm-and held that continuity is interrupted by "relinquishment of both actual and constructive possession of the gun before it is reacquired." 711 F.3d at 378 (citation and alteration omitted). Applying our reasoning in Benjamin to § 841, we conclude that possession of 1000 grams of heroin begins when a defendant has the power and intention to exercise dominion and control over all 1000 grams, and ends when his possession is interrupted by a complete dispossession or by a reduction of that quantity to less than 1000 grams.
The Government's evidence supporting the 1000-gram verdict was premised on its incorrect belief that it could combine weights from multiple distributions and discontinuous possessions during the indictment period. The Government acknowledged *761its error at oral argument, Oral Arg. at 18:32, but asserted that even so, it had presented sufficient evidence to support a reasonable inference that at some point during the indictment period, Rowe possessed at least 1000 grams of heroin with intent to distribute. We are unconvinced. If we assume that the jury did not combine the amounts distributed or possessed over time, and instead sought to determine whether Rowe possessed a 1000-gram quantity of heroin at least once during the indictment period, the Government's evidence was not sufficient to permit any rational juror to make such a finding beyond a reasonable doubt.
From Pierce's testimony about his first encounter with Rowe, a rational juror could have inferred that: (1) there were up to eight packages in Rowe's black bag; (2) each package contained up to 100 grams of a substance; and (3) based on the confusion between the twenty-eight gram and twenty-one gram packages, two or more packages contained heroin. Assuming, based on Pierce's testimony about the markings on the bags, that at least one bag was marked "50," one was marked "75," every other bag was marked "100," and adding that to the twenty-one grams Rowe possessed before distributing that package to Pierce, a rational juror could conclude that Rowe possessed and intended to distribute 746 grams of heroin. No rational juror could have found beyond a reasonable doubt, based on this testimony, that Rowe possessed 1000 grams or more of heroin at that time.
Nor did Special Agent Shuffelbottom's expert testimony fill the evidentiary gap. Special Agent Shuffelbottom opined that a dealer who could sell 200 grams of heroin at a time (as the evidence showed Rowe did) would have access to multi-kilogram quantities. However, testimony about the amount of heroin that dealers generally would be able to access is insufficient to support a finding that Rowe had constructive possession of 1000 grams of heroin at any particular time. This evidence might be a basis for speculation, but it is not proof beyond a reasonable doubt.
The ledger corroborated Pierce and Special Agent Shuffelbottom's testimony, but failed to provide the necessary logical step between Rowe's discrete distributions and possessions and an instance of possession of 1000 grams of heroin. The Government's theory was that all of the notations in the ledger referred to heroin Rowe distributed during the indictment period. Yet, despite its obvious evidentiary value, the ledger lacked dates. Without details about the timing of transactions, a rational juror would only have been able to speculate about whether Rowe possessed a quantity of at least 1000 grams at one time during the indictment period.
All of the evidence-including Pierce's testimony, Special Agent Shuffelbottom's testimony, and the ledger-was insufficient, even considered in the light most favorable to the Government, to allow a rational juror to find that Rowe possessed at least 1000 grams of heroin at a single time with the intent to distribute it. We will therefore vacate the conviction as to the 1000 grams of heroin.
We further note that where, as here, the Government's presentation of the evidence rested upon an incorrect understanding of the offense, the District Court failed to correct the error by instruction, and the general verdict does not assist this Court in understanding how the jury arrived at its determination, we are reluctant to proceed as though the jury was not misled. See Caraballo-Rodriguez , 726 F.3d at 431. Deference to jury verdicts is premised on an expectation that jurors "are instructed extensively as to what evidence they can consider, how to consider it, and ... the relevant legal principles." Id. That did not happen here, and the logic of *762Caraballo-Rodriguez provides additional support for our decision to vacate.6
B. Sentencing Error
Rowe challenges the District Court's acceptance of the drug weight calculation in the PSR. The Government agrees that the District Court erred in adopting that calculation.7 Having reviewed the District Court's sentencing determination, we also conclude that the court abused its discretion by basing its determination on unsupported drug weight assertions.8 Therefore, we will vacate the sentence. What remains is the parties' dispute about whether, on remand, the Government should be permitted to develop the record on the drug weight issue.
At sentencing, "the government bears the burden of proof by a preponderance of the evidence," United States v. Brothers , 75 F.3d 845, 848 (3d Cir. 1996) (citation omitted), and ordinarily is only *763afforded one opportunity to carry its burden. United States v. Dickler , 64 F.3d 818, 832 (3d Cir. 1995). We have recognized a limited exception to our distaste for "a second bite at the apple," id. (quoting United States v. Leonzo , 50 F.3d 1086, 1088 (D.C. Cir. 1995) ), when the Government "has tendered a persuasive reason why fairness ... requires" that the sentencing court "provid[e] the government with an additional opportunity to present evidence on remand." Id. In Dickler , we imagined such an exception would apply where "the government, for want of notice or any other reason beyond its control, does not have a fair opportunity to fully counter the defendant's evidence." Id.
At oral argument, the Government conceded that Dickler stands for the proposition that the Government should not generally receive a second opportunity to present evidence for sentencing absent a persuasive reason, but was unable to offer one. Oral Arg. at 28:58. We do not perceive any such reason, and therefore the Government will not be permitted to introduce additional evidence regarding drug quantity. It may argue for any sentence supported by the existing record.
III.
For the reasons explained above, we will vacate the judgment of conviction for distribution and possession with intent to distribute 1000 grams or more of heroin, and we will remand to the District Court for entry by the Court of a judgment of conviction for distribution and possession with intent to distribute 100 grams or more of heroin. We will also vacate the sentence and remand for re-sentencing. Upon re-sentencing, the Government may not introduce new evidence to prove drug quantity.