PER CURIAM.
Tommy “Tylee” Henry (“Henry”) appeals his conviction for conspiracy, and Herman Rosenboro (“Rosenboro”) appeals his conviction for conspiracy and distribution of cocaine powder and cocaine base, also called “crack” or “crack cocaine.” Henry challenges (1) the sufficiency of the [495]*495evidence; (2) the district court’s decision to allow a police officer to testify, on short notice to the defense, regarding a statement Henry made to the officer; and (3) the district court’s decision to exclude an expert witness. Rosenboro challenges (1) the district court’s decision to exclude an expert witness; (2) the district court’s refusal to grant him a downward departure in sentencing for poor health; and (3) the government’s alleged failure to strictly comply with the notice requirements of 21 U.S.C. § 851, which requires the government to notify the defense, prior to trial, of its intention to seek a statutorily enhanced sentence. We AFFIRM the judgment of the district court on all grounds.
I.
Henry and Rosenboro (collectively “Appellants”) are accused members of a larger cocaine distribution conspiracy formerly headed by Gerald Scott Long (“Long”), a major cocaine hydrochloride (“cocaine powder” or “cocaine”) supplier in the upper East Tennessee region for many years. Long, who started selling in 1989, bought his cocaine in Florida and elsewhere, and by 1996 he was paying from $16,500 to $23,000 per kilogram. Long estimated that in the period between 1996 and 2000 — the time alleged in this conspiracy — he purchased forty or more kilograms. In his plea agreement, he stipulated to conspiring to distribute between fifty and 150 kilograms of cocaine powder. He had a number of sellers, including Kevin Evans (“Evans”), Randy Carpenter (“Carpenter”), Jeff Teague (“Teague”), Jonathan Lytle (“Lytle”), and Marcus Thompson (“Thompson”).
A. Henry’s Involvement
Long recruited his eighteen-year-old relative Henry in the summer of 1998, and Henry sold cocaine for Long from that time until Long’s arrest on April 19, 2000. Long began by distributing ounces of cocaine to Henry on a weekly or bi-weekly basis and later alternated between ounces and quarter-kilograms. Henry, who was at times Long’s biggest seller, would pay for the cocaine either at the time he received it or else after he had sold it.
Long would occasionally pool his money with Henry, Evans, Teague, Lytle, and others — a total of $50,000 to $80,000, depending on the occasion — to buy large quantities of cocaine in Florida. Henry accompanied Long on two or three of these Florida buying trips. Long would do the buying himself, because his suppliers preferred not to have anyone else involved. On one such trip, Long, Henry, and Lytle had traveled together, Long carrying $80,000 of his own money, but it turned out that the cocaine Long purchased was fake, and he lost $51,000 in cash on the deal. On the date of Long’s arrest, April 19, 2000, Long was trying to purchase twenty-two kilograms of cocaine by paying $80,000 up-front in pooled cash: Henry had contributed $5,000; Evans, $8,000; Teague, $5,000; and Long, $62,000. Henry continued to sell after Long’s arrest (in transactions described below), though he obviously needed another supplier.
One of Henry’s regular customers was Billy Joe Wolfe (‘Wolfe”), who had known Henry for most of his life. Between 1996 and 2000, Wolfe purchased cocaine and crack from Henry, cocaine from Long and Evans, and crack from Lytle. On one occasion, in the summer of 1999, Henry approached Wolfe as the latter was leaving a recreation center; they got into Wolfe’s car, where Henry showed Wolfe a bag containing over an ounce of crack, and Wolfe bought $250 worth.
Wolfe, who was both a user and a seller, was arrested in October 1999, while in [496]*496possession of two ounces of cocaine, and he thereafter agreed to work for the police as a confidential informant. As an informant, Wolfe bought cocaine from Henry on four different occasions in the year 2000 — July 19, July 22, August 9, and September 6— for a total of about sixty-three years. On the final occasion, Henry retrieved some cocaine from his grandmother’s house; he met Wolfe outside the house; they drove a short distance; and Henry exchanged 15.8 grams2 of cocaine for $1,400.
Also on September 6, 2000, a Kingsport Police Department patrol officer stopped a vehicle in which Henry was a passenger. After Henry had exited the car, the officer asked him if he was carrying any contraband or anything illegal and whether he (the officer) might search Henry. Henry consented to a search, and, according to the officer,
he laughed and told me that ... [”]I won’t be holding anything, I’m too big for that. You know I’m too big for that.[”] ... He said, [”]I might distribute, but you know I don’t hold, ... you may catch me on a conspiracy one day, but you know you won’t catch me holding.[”]
The officer found a wad of cash containing at least two to three hundred dollars, but he let Henry go because he had insufficient reason to arrest him.
Henry was finally arrested on January 9, 2001, in Kingsport, Tennessee, at the apartment of a woman named Erica Davis. While Henry was inside, the police used a drug interdiction dog to examine a GMC Yukon Sport Utility Vehicle registered to Henry and his mother, the same vehicle that the officers had seen Henry driving previously. After the dog alerted on the truck, the officers searched it. Inside a duffle bag sitting on the front passenger’s seat, they found a basketball jersey bearing Henry’s nickname “Sweet Lee,” $5,720 in cash stuffed into a pair of tennis shoes, and a Rolex wristwatch, a gold chain, and a bracelet — together worth several thousand dollars. (The money and the value of the jewelry are significant because Henry’s regular job was at a gas station.) Elsewhere in the vehicle they found a bottle of Inositol, which drug dealers often use to dilute cocaine (e.g., to cheat customers); a strainer, useful in breaking up pieces of cocaine; a wireless telephone; a pager; and an electronic address book.
B. Rosenboro’s Involvement
Another alleged member of the conspiracy was Rosenboro, a relative of Henry who had also sold cocaine to Wolfe both before and after Wolfe’s arrest. On February 15, 2000, the police wired Wolfe and sent him to the Kingsport, Tennessee, Amoco gas station where Henry worked. The objective that day was to catch Henry; hence, when Wolfe arrived at the station, he asked Rosenboro, who also worked there, if Henry was around. Rosenboro told him that Henry had “gone to see the tax man,” but offered to do the deal himself. Wolfe told Rosenboro that he wanted to buy an ounce of cocaine; Rosenboro replied that he could get two “nice ones” [perhaps “eight balls,” 3.5-gram units of cocaine] for Wolfe within fifteen minutes and bragged that he was selling ten to twelve ounces at the station per week. When Wolfe discovered, after Rosenboro made a phone call, that it would be a few hours before Rosenboro could get the amount Wolfe wanted, Wolfe instead [497]*497bought what Rosenboro had ready — 1.4 grams of crack at $850. The police tape-recorded the transaction, as they did all transactions involving Wolfe as an informant.
The next day, February 16, 2000, the officers gave Wolfe $750 and sent him back to the Amoco station, where he again sought to buy an ounce from Rosenboro. The two drove to Rosenboro’s house, from which Rosenboro retrieved 6.5 grams of cocaine that Wolfe purchased for $750. When Wolfe questioned whether Rosenboro was selling him the stated quantity (either seven grams or 10.5 grams — it was not clear), Rosenboro assured him that he had been selling 3.5-gram “eight balls” of cocaine for $300 all day.
A couple weeks later, on March 3, 2000, Wolfe again drove to the Amoco station and asked for Rosenboro. When Rosenboro appeared, he got into Wolfe’s car and sold him 1.5 grams of crack for $700. Before making the purchase, Wolfe questioned whether the quantity was worth $700, observing that Henry would have delivered twice as much cocaine for the same money; Rosenboro was skeptical, telling Wolfe that Henry himself had divided out the quantities for Rosenboro the night before.
On June 19, 2000, Rosenboro called Wolfe to ask whether he wanted to purchase two ounces of cocaine. Wolfe, after making arrangements with the police, met with Rosenboro on June 20, 2000, in the parking lot of a local hospital. Rosenboro got into Wolfe’s car, telling him that he did not have the cocaine with him because he had had twenty ounces to sell and needed to be careful. Rosenboro directed Wolfe to drive to an adjacent parking lot, where Rosenboro’s wife was waiting in their truck; Rosenboro walked out to the truck and soon returned, selling Wolfe 27.8 grams of cocaine for $1,500. Again Wolfe disputed the drug quantity. Rosenboro told him to take it or leave it, apparently because he had sold his other nineteen ounces earlier in the day, and this was his last ounce. Rosenboro also told Wolfe that he would have more cocaine later that night.
In addition to Wolfe’s informant work, the testimony of Lytle, one of Long’s aforementioned buyers, also connects Rosenboro to the conspiracy. Lytle had seen both Henry and Rosenboro selling in the same neighborhood and knew that Long provided their cocaine. Lytle had also sold cocaine, apparently in small amounts, to Rosenboro on more than one occasion. Additionally, at one point during the investigation in 2000, Wolfe went to the Amoco station and asked Rosenboro for some cocaine; Rosenboro directed Wolfe to Lytle, who talked with Wolfe about a potential cocaine transaction.
II.
On December 13, 2000, a superseding indictment charged Henry and Rosenboro - along with Lytle, Evans, Teague, and Marsh — with conspiracy to distribute over five kilograms of cocaine and over fifty grams of crack between August 1996 and November 15, 2000. Additionally, Henry was charged in counts 27-30 with cocaine distribution, and Rosenboro was charged in counts 17-19 and 26 with distribution of cocaine and crack. On February 26, 2001, the government filed a notice with the court of its intention to seek an increased punishment for Rosenboro, based on his prior drug convictions for selling heroin and possessing cocaine.
On the morning of April 17, 2001, the first day of Henry’s joint trial with Rosenboro, Henry pleaded guilty on his substantive counts and went to trial on the conspiracy charges only. Two days later, the [498]*498jury found Henry and Rosenboro guilty of conspiracy and Rosenboro guilty of the four substantive offenses charged.
On April 30, 2001, Henry filed a motion for a new trial, which the district court denied on November 29, 2001. Rosenboro filed a motion for a new trial on May 1, 2001, requesting additionally that he be allowed to make an offer of proof regarding two expert witnesses the court had not allowed to testify. On June 1, 2001, the court granted the offer of proof motion as to one witness but not the other, and it denied the new trial motion. Two-and-a-half months later, on August 13, 2001, Rosenboro filed the offer of proof, along with a motion to reconsider his motion for a new trial, but the court dismissed these as untimely.
On December 3, 2001, the trial judge sentenced Henry to 121 months in prison and five years supervised release on each count, to run concurrently, and Rosenboro to life in prison on count one, 135 months on each of the four substantive counts, and six years supervised release on each count, all of which would run concurrently.
III.
A. Whether There was Sufficient Evidence to Convict Henry for Conspiracy to Distribute Fifty Grams of Cocaine and Crack
Henry argues that there was insufficient evidence to support the jury’s verdict that he was part of a conspiracy to possess and distribute over fifty grams of crack. He does not dispute the jury’s finding that he was part of a conspiracy to possess and distribute over five kilograms of cocaine.
“The relevant question in determining the sufficiency of the evidence to support a guilty verdict is whether ‘after viewing the evidence in the light most favorable to the prosecution, any rational trier of fact could have found the essential elements of the crime beyond a reasonable doubt.’ ” United States v. Clark, 928 F.2d 733, 736 (6th Cir.1991) (quoting Jackson v. Virginia, 443 U.S. 307, 319, 99 S.Ct. 2781, 61 L.Ed.2d 560 (1979)). When considering the sufficiency of the evidence, the court does not weigh the evidence or assess the credibility of the witnesses. United States v. Jackson, 55 F.3d 1219, 1225 (6th Cir.1995). The government may meet its burden through circumstantial evidence alone, and such evidence need not exclude every possible hypothesis except that of guilt. United States v. Peters, 15 F.3d 540, 544 (6th Cir.1994).
To prove a drug conspiracy under 21 U.S.C. § 846, “the government must prove that a conspiracy existed, that the accused knew of the conspiracy, and that he knowingly and voluntarily joined it.” United States v. Ledezma, 26 F.3d 636, 640 (6th Cir.1994) (internal quotation marks and citations omitted). The connection between the defendant and the conspiracy only has to have been slight, and there need not have been an explicit agreement — a tacit understanding, demonstrated through circumstantial evidence, will suffice. Id. Drug conspiracies are often chain conspiracies, in which the drugs are sold down the line between buyers and sellers; to find a conspiracy in such cases, it is not necessary to determine that each participant knew, or was involved with, all other levels, but it is necessary to find that each individual knew he was participating in a joint enterprise. Id.; see also United States v. Bourjaily, 781 F.2d 539, 544 (6th Cir.1986) (“One can assume that participants understand that they are participating in a joint enterprise because success is dependent on the success of those from whom they buy and to whom they sell.”).
[499]*499Count one of the indictment in this case was worded in the conjunctive: the conspiracy was to distribute the cocaine and the crack. At trial, the government asked the court to word the jury instructions for this count disjunctively, but the court worded its instructions conjunctively, telling the jury that “if you find that each of the defendants was involved in a conspiracy to distribute both at least 5 kilos of cocaine and at least 50 grams of crack, you may return a unanimous verdict of guilty ... in regard to count number 1” (emphasis added). After the judge sent the jury away to deliberate, the Assistant United States Attorney (“AUSA”) - concerned because the government could not appeal if the jury found against it on count one - brought up the eonjunctive/disjunctive issue again and discussed it for some time, asking the court to change the jury form. However, in the end the court concluded that it would be “a violation of the English language” to transform a conjunctive indictment into a disjunctive jury instruction; since the indictment was conjunctive, the jury’s finding had to be conjunctive. Of course the government’s concerns became moot, because the jury found Henry guilty on count one.
Henry asserts that in order to support a guilty verdict, the government was required to establish both drug types beyond a reasonable doubt, given the government’s decision to plead in the conjunctive rather than separating the conspiracy counts into separate counts for each drug type and quantity.
In United States v. Dale, 178 F.3d 429 (6th Cir.1999), the defendant, Dale, was charged with a single count of conspiring to distribute crack and marijuana. The court instructed the jury that it would have to find against Dale on either the crack or the marijuana conspiracy. After the jury ruled against Dale in a general verdict that did not specify whether it had found against him on crack or marijuana or both, the court sentenced Dale based on the crack finding, which provided for a maximum sentence of forty years, significantly longer than the five-year maximum for marijuana. Id. at 432. On appeal, Dale challenged the sentence he received but not the underlying conviction, arguing that the court should have applied the five-year maximum. This court agreed, following a Supreme Court case that implied that “the shorter maximum sentence should be used if the verdict is merely general, rather than specific, and the one drug allows for a sentence above the maximum for another charged drug.” Id. at 433 (construing Edwards v. United States, 523 U.S. 511, 118 S.Ct. 1475, 140 L.Ed.2d 703 (1998)). Having found that the district court had plainly erred, we remanded the case. See also United States v. Randolph, 230 F.3d 243, 252 (6th Cir.2000) (following Dale).
In United States v. Neuhausser, 241 F.3d 460 (6th Cir.2001), the defendant, Neuhausser, was convicted of conspiracy to distribute cocaine and marijuana. Arguing that the court erred by sentencing him under the cocaine guidelines, which resulted in a sentence exceeding the ten-year maximum applicable under the marijuana guidelines, Neuhausser challenged his sentence but not his conviction on the basis of Dale. Id. at 468. However, we did not find Dale dispositive, because in this case the district court - tracking the language of the indictment - had worded its instructions conjunctively; hence, the jury’s general verdict unambiguously found Neuhausser guilty of both types of conspiracy. Id. at 469-70.
The government correctly distinguishes Dale and Neuhausser from the present case in that the former two concerned challenges solely to the sentence, not to [500]*500the underlying conviction. Moreover, both Dale and Neuhausser support the conclusion that a general guilty verdict conviction on a multiple-object conspiracy charge will stand despite insufficient evidence to support conviction as to all but one of the objects. See Griffin v. United States, 502 U.S. 46, 56-57, 112 S.Ct. 466, 116 L.Ed.2d 371 (1991) (noting that “[w]hen a jury returns a guilty verdict on an indictment charging several acts in the conjunctive ... the verdict stands if the evidence is sufficient with respect to any one of the acts charged,” and holding that this also applies to multiple-object conspiracies) (quoting Turner v. United States, 396 U.S. 398, 420, 90 S.Ct. 642, 24 L.Ed.2d 610 (1970)); see also Dale, 178 F.3d at 432 (quoting and following Griffin in regard to Dale’s substantive conspiracy conviction). Consequently, Henry’s conviction on count one stands if there was sufficient evidence as to either cocaine or crack. Since he does not challenge the sufficiency of his conviction in regard to cocaine, Henry’s claim that the evidence is insufficient to convict him on count one is without merit.
Furthermore, unlike in Dale and Neuhausser, there is no disparate sentencing issue here. The district court sentenced Henry based on the cocaine amount. Had the district court looked to the crack amount instead, however, the sentencing would have been the same, because the statutory sentencing ranges for both five kilograms of cocaine and fifty grams of crack are identical: ten years to life. See 21 U.S.C. § 841(b)(l)(A)(ii)-(iii). Similarly, according to the applicable United States Sentencing Guidelines (“USSG”) provision, USSG § 2D1.1, a defendant held responsible for at least five kilograms but less than fifteen kilograms of cocaine should be sentenced at the base offense level of 32, and a defendant held responsible for at least fifty grams but less than 150 grams of crack should also receive a base offense level of 32. USSG § 2D1.1(4).
B. Whether the District Court Erred by Allowing the Government to Present a Statement Henry Had Made to a Local Police Officer During a Traffic Stop
As noted above, on September 6, 2000, Henry said some incriminating things to a Kingsport Police Department patrol officer, volunteering that “I might distribute, but you know I don’t hold [drugs], ... you may catch me on a conspiracy one day, but you know you won’t catch me holding.” The officer was not part of the federal investigation team, nor was the stop related to the federal investigation. The AUSA learned of the statement on Monday, April 16, 2001, the day before the trial began. His office called Henry’s counsel’s office at around 3:00 pm that day (Monday), telling them that a packet of “Jencks Act” discovery material would be available at 4:00 pm. See 18 U.S.C. § 3500 (the Jencks Act, providing that “in any criminal prosecution brought by the United States, no statement or report in the possession of the United States which was made by a Government witness or prospective Government witness (other than the defendant) shall be the subject of subpoena, discovery, or inspection until said witness has testified on direct examination in the trial of the case.”). Around 4:00 pm, Henry’s counsel’s office had a messenger pick up the packet, which included the officer’s police report summarizing Henry’s comments; on top of the packet, a small stick-on note read “Giglio and Jencks.” See Giglio v. United States, 405 U.S. 150, 153-54, 92 S.Ct. 763, 31 L.Ed.2d 104 (1972) (holding that the prosecution’s failure to disclose material information regarding the reliability of a government witness violates due process). According to Henry, there was no letter or other notice with the materials [501]*501indicating that the government intended to use the statement in its case in chief, and defense counsel discovered the police report containing the statement by chance when looking for Jencks material in preparation for cross-examination of the witnesses that the government called the first day of trial.
Henry’s counsel did not bring the late-notice problem to the district court’s attention by filing a motion in limine or a motion to suppress or for a continuance. Instead, when the government presented the officer to testify on Wednesday, the second day of the trial, Henry’s counsel asked to address the court without the jury present. Henry’s counsel then complained of the late notice, argued that it was a violation of Rule 16 of the Federal Rules of Criminal Procedure and Brady v. Maryland, 373 U.S. 83, 83 S.Ct. 1194, 10 L.Ed.2d 215 (1963), and suggested that the proper remedy was to exclude the witness. The court refused to exclude the officer entirely but offered to grant a continuance. When it became clear that Henry’s counsel did not want a continuance,3 the court overruled counsel’s objection and let the officer testify immediately. On appeal, Henry argues that the district court’s admittance of the officer’s testimony violated Rule 16 and Brady.
This court reviews a district court’s discovery rulings for an abuse of discretion. United States v. Quinn, 230 F.3d 862, 866 (6th Cir.2000). Rule 16(a)(1)(A) of the Federal Rules of Criminal Procedure requires the government to disclose upon request “that portion of any written record containing the substance of any relevant oral statement made by the defendant whether before or after arrest in response to interrogation by any person then known by the defendant to be a government agent,” and to disclose any “oral statement made by the defendant whether before or after arrest in response to interrogation by any person then known by the defendant to be a government agent if the government intends to use that statement at trial.” Fed.R.Crim.P. 16(a)(1)(A).
Henry argues that the government violated Rule 16 in two ways: (1) its disclosure should have highlighted the fact that it contained an incriminating statement by Henry, and it should have indicated that the government intended to call the officer as a witness; and (2) if the government had exercised due diligence, the statement would have been within its knowledge and control months before trial because the officer who heard it was a government agent.
Regarding Henry’s first objection - which he did not raise before the district court - Henry cites no cases in support of his proposition that these “failures” violated Rule 16. The court sees no reason to read such requirements into the Rule, and we conclude that his argument fails. See also Gov’t Br. at 36 (“The Rule states that disclosure must occur ‘if the government intends to use that statement at trial.’ This language creates a prerequisite for disclosure, not an obligation on the part of the government.”). Regarding Henry’s second objection, he cites United States v. Bailleaux, 685 F.2d 1105 (9th Cir.1982), which held that the AUSA with due diligence should have discovered a recorded statement made by the defendant well before trial, because the FBI - part of “the government” - was in possession of the tape. Id. at 1113. The government argues, in reply, that the state officer who testified in the present case was not a [502]*502member of the federal government, nor was he a part of the federal investigation against Henry, and the AUSA was the first federal agent to learn of Henry’s statement to the officer. We agree with the government that it makes little sense here to impute to the AUSA what was known by this state police officer. See also United States v. Stewart, No. 95-6188, 1997 WL 90311, at *2 (6th Cir. Feb.28, 1997) (finding no Rule 16 violation where “the government first learned of the search during a trial recess, when a Kentucky police officer brought the matter to the prosecuting attorney’s attention,” and “[t]he prosecuting attorney immediately apprised defense counsel of this discovery”).
Henry also contends that, according to Brady, “the government had an obligation under the Due Process Clause of the Fifth Amendment to disclose the statement which went directly to the defendant’s guilt or innocence.” Henry Br. at 23. The government accurately points out, though, that “Brady is concerned almost exclusively with the prosecution’s failure to turn over material rather than mere delay and, more importantly here, Brady is concerned with exculpatory evidence, that is[,] evidence favorable to the defendant.” Gov’t Br. at 36; see also Moore v. Illinois, 408 U.S. 786, 794-95, 92 S.Ct. 2562, 33 L.Ed.2d 706 (1972); United States v. Bencs, 28 F.3d 555, 560-61 (6th Cir.1994). Henry’s statement was not only inculpatory, but was also made available to Henry. We conclude that Henry’s argument fails.
C. Whether the District Court Erred by Not Allowing Henry or Rosenboro to Have an Expert Testify About How Cooperating Witnesses Have a Motive to Lie
Several of the government’s main witnesses against Henry and Rosenboro - namely, Long, Lytle, and Evans - were testifying pursuant to plea agreements and were eligible to benefit from their cooperation in testifying. When cross-examining these witnesses, counsel for Appellants pressed the witnesses to divulge what they expected their sentences to be without any reduction, and what reduction they expected to receive as a result of their testimony, but Long and Lytle were unwilling to say anything definite. Evans, however, testified that his unreduced expectation was 168 months and his reduced expectation was 100 months. Wolfe had not been charged for the two ounces that police caught him with in 1999, and he hoped ultimately to receive nothing worse than probation.
Appellants’ counsel wanted to combat the recalcitrance of Long and Lytle by introducing the expert testimony of Gerald Gulley (“Gulley”), an experienced Criminal Justice Act attorney, who would talk about the sentences the two witnesses were facing under the USSG and how they stood to benefit from reductions. Gulley took the stand, but before Henry’s counsel had explained Gulley’s purpose, the court interrupted, saying that it was not proper for him to testify about the sentences of Appellants before they had even been found guilty. Henry’s counsel explained that Gulley would testify about the sentences of the witnesses for the purpose of credibility, but the district court rejected Gulley because Appellants’ prospective sentences were “not a proper matter for the jury to take up.”
Rosenboro had also subpoenaed David Nanney (“Nanney”) of the U.S. Probation Office, who was supposed to offer testimony similar to Gulley’s. According to Rosenboro, the district court quashed this subpoena off the record and did not allow [503]*503Rosenboro to make an offer of proof, even though the court had allowed Nanney to testify similarly in another drug conspiracy case, United States v. Runyan A district court memorandum filed after the verdict explains the situation further: Nanney, a court employee, had approached the judge and told him that defense counsel had issued a subpoena whereby Nanney was “to calculate the guideline range for a number of the cooperating witnesses,” and the district court quashed the subpoena because it considered this assignment overly burdensome, potentially speculative, and likely to result in the improper disclosure of confidential information.
After trial Rosenboro filed a motion for a new trial, based on the exclusion of Gulley and Nanney, and asked the court for permission to submit offers of proof in the form of affidavits from the two experts. The court allowed Rosenboro to submit an offer of proof with regard to Gulley but not to Nanney. The court also denied Appellants’ motions for a new trial on the exclusion-of-expert-witness grounds, explaining that
[a]t trial, the defendant contended that the testimony of Gerald Gulley was needed for the purpose of demonstrating to the jury the application of the guidelines in circumstances where the charged individual receives a sentencing benefit pursuant to their plea of guilty. However, any motion for downward departure based upon the substantial assistance of a defendant must be filed by the government, and is granted or denied in the Court’s discretion, with the Court having the option of setting a sentence that departs from the guideline range.
Consequently, there is no reason to ask Mr. Gulley any hypothetical guideline questions regarding the benefit cooperating witnesses will receive in regard to their substantial assistance, because substantial assistance is immaterial to the calculation of a defendant’s guideline range, and Mr. Gulley could only speculate in regard to what the United States Attorney or the Court could do.
Appellants now argue that the district court committed reversible error by excluding Gulley and Nanney.
This court reviews for an abuse of discretion a trial court’s determination of whether to admit expert testimony. United States v. Bender, 265 F.3d 464, 472 (6th Cir.2001). The admission of expert testimony is governed by Federal Rule of Evidence 702: “If scientific, technical, or other specialized knowledge will assist the trier of fact to understand the evidence or to determine a fact in issue, a witness qualified as an expert by knowledge, skill, experience, training, or education, may testify thereto in the form of an opinion or otherwise.” Fed.R.Evid. 702.
The most relevant Sixth Circuit case is United States v. Thomas, 74 F.3d 676 (6th Cir.1996), in which a panel considered a district court’s refusal to allow defense counsel “to introduce testimony from ‘an experienced federal criminal practitioner’ about the incentive a person such as [the witness] would have to give false testimony as a result of a plea agreement containing a promise of a reduced sentence in exchange for cooperation with the government.” Id. at 683. This court found that “the district court ... did not abuse its discretion by finding that the jury could fully understand, without expert testimony, the incentive a government witness might have to lie under oath, and that therefore the proposed testimony would not be helpful to the jury here.” Id. at 683-84. Citing another element in favor of the district court, it noted that the court had instructed the jury that it should treat [504]*504the witness’s statement with caution. Id. at 684. Significantly, the court also held that “in light of the defendant’s ability to cross-examine [the witness] and the district court’s cautionary jury instruction, even if the district court had erred by disallowing the expert testimony, any error would be harmless.” Id.
Henry argues that Thomas is inapplicable here because the purpose of the expert opinion was to demonstrate the witnesses’ motives to testify against Henry, rather than to give an opinion on whether or not any or all of the witnesses were credible. Regardless of Appellants’ proffered intentions, they cite no case, nor does this court know of any, in support of their proposition that such an exclusion constitutes an abuse of discretion and prejudicial error. Given that the district court here allowed Appellants to examine and discuss credibility in this regard at length and also issued cautionary jury instructions regarding witness testimony, we find neither abuse of discretion nor prejudicial error. See also United States v. Johnson, 297 F.3d 845, 861-62 (9th Cir.2002) (finding no prejudice where the court excluded an expert witness who would have testified about the prospective sentences of government witnesses); United States v. French, 12 F.3d 114, 117 (8th Cir.1993) (“Given the substantial-assistance provision, it is clearly within the realm of common sense that certain witnesses would have an incentive to incriminate the defendant in exchange for a lower sentence. Expert testimony is not necessary to draw this conclusion. The credibility of witnesses is a determination for the factfinder ... to make. The jury should be allowed to use its common sense.”); United States v. Wooten, No. 984697, 2000 WL 102958, at *2 (4th Cir. Jan.31, 2000) (“Wooten has offered no authority that supports the admission of expert testimony on the application of the sentencing guidelines. The record reflects that Wooten’s counsel thoroughly cross-examined the co-conspirators with respect to their expectation of receiving motions to depart based upon substantial assistance, and their resulting incentive to lie. As credibility is a matter soundly within the jury’s understanding, the district court did not abuse its discretion by concluding that the expert testimony proffered by Wooten was unnecessary.”).
Henry also argues that the district court’s denials violated his constitutional rights to confront witnesses and to present a complete and meaningful defense. Nevertheless, he provides no reason for this court to conclude that the situation here rises to such constitutional dimensions, and we conclude that this claim fails.
D. Whether the Evidence Was Sufficient to Convict Rosenboro of Conspiracy and Distribution of Cocaine and Crack
Rosenboro contends that the evidence against him on the conspiracy and distribution charges was insufficient because Wolfe, who was testifying for his own benefit, was the only person who actually saw Rosenboro hand over drugs in any of the alleged transactions and because Long and Lytle both testified that they were not involved with Rosenboro. But Wolfe’s credibility was an issue for the jury rather than this court, and the evidence against Rosenboro — even without the officers’ direct visual observations— was iron-clad, in the form of recorded statements and before-and-after visual and physical evidence. We conclude that this argument fails.
E. Whether the District Court Erred by Not Reducing Rosenboro’s Sentence Due to His Medical Condition
Rosenboro apparently has significant health problems. His presentence report, for example, notes that
[h]e is presently on a waiting list for a kidney transplant, and suffered renal [505]*505shutdown approximately four years ago. The defendant is also diagnosed with diabetes, and has been insulin dependent for the past 15 years. He is legally blind, and has a total loss of vision in his left eye.
He argues that the district court erred by failing to depart below his mandatory term of life imprisonment pursuant to 21 U.S.C. § 841(b)(1)(A), given the suggestions found in USSG § 5H1.4:
Physical condition or appearance, including physique, is not ordinarily relevant in determining whether a sentence should be outside the applicable guideline range. However, an extraordinary physical impairment may be a reason to impose a sentence below the applicable guideline range; e.g., in the case of a seriously infirm defendant, home detention may be as efficient as, and less costly than, imprisonment.
Rosenboro filed a motion for a downward departure on these grounds with the district court, but the court ruled that it lacked authority to “depart below a statutory minimum sentence except in the case of a substantial assistance motion under 18 U.S.C. § 3553(e).” A district court’s refusal to depart is not appealable, unless the court erroneously believed that it lacked authority to do so. United States v. Salgado, 250 F.3d 438, 460 (6th Cir.2001). It is well-established that a district court lacks discretion to impose a sentence below a statutory mandatory minimum, unless (1) the government files a motion for a downward departure under 18 U.S.C. § 3553(e), or (2) the defendant qualifies for the safety-valve provisions of 18 U.S.C. § 3553(f). See Burke, 237 F.3d at 745 (“In the absence of one of the exceptions set out in §§ 3553(e),(f), or such other similar exceptions as Congress may create, defendants may not be sentenced, by means of a downward departure, to a term of imprisonment or other punishment below the minimum imposed by the statute under which they were convicted.”). In this case it is undisputed that the government did not file for a downward departure under § 3553(e), and Rosenboro does not qualify for § 3553(f) because he had more than one criminal history point. Consequently, Rosenboro’s claim must fail.
F. Whether the Government Violated 21 U.S.C. § 851’s Notice Requirements
To statutorily enhance a defendant’s drug sentence with a prior conviction, the government must first comply with 21 U.S.C. § 851, which requires the government “before trial, or before entry of a plea of guilty,” to “file [ ] an information with the court (and serve [ ] a copy of such information on the person or counsel for the person) stating in writing the previous convictions to be relied upon.” 21 U.S.C. § 851(a)(1) (emphasis added); see also United States v. Mans, 999 F.2d 966, 969 (6th Cir.1993) (noting that “the requirements of § 851(a)(1) apply only to statutory sentence enhancement, not sentence enhancement under ... the Sentencing Guidelines”). In the present case the government sought an enhanced sentence against Rosenboro, because in 1974 he had received a ten-to-fifteen-year sentence for three counts of selling heroin, and in 1990 he had received ten years for two counts of selling crack. The enhancement promised to make a big difference in Rosenboro’s sentence, potentially increasing a ten-year sentence to a life sentence.
On February 23, 2001 (approximately two months before trial), the AUSA faxed Rosenboro an Information notifying him that, should Rosenboro be convicted, the government would be seeking an enhanced sentence based upon Rosenboro’s prior convictions. The Information, however, was not signed, and it was sent along with a proposed plea agreement. Rosenboro contends that it appeared as if the Government was sending the unexecuted docu[506]*506ment as a threat, i.e., the government would file the Notice if Rosenboro refused to sign the plea agreement. On February 26, 2001, three days after sending the fax, the AUSA submitted the same § 851 Information to the district court — properly signed — along with a certificate averring that the government had served the Information on Rosenboro’s counsel. Although the AUSA also mailed this signed Information to Rosenboro’s counsel, Rosenboro’s counsel attests that he never received it.
Rosenboro did not complain about the lack of a signed copy of the Information before trial — a failure that his counsel explains thus:
I expected that I would receive an executed § 851 Notice. In the last few days before the trial, this issue came to the forefront of my thoughts. I assumed that since I had received no executed Notice of Enhancement, the Government had forgotten to file it. If that assumption had been correct, it would have been a tremendous disservice to my client to ask the Government, “Hey, are you going to file that Notice of Enhancement?”
Rosenboro also did not complain of the alleged failure to comply with § 851 in his initial objection to the presentence report, even though the report recommended the prior-convictions enhancement. Instead, he first complained about the absence of an executed Information in a motion to reconsider the court’s order denying his objection to the presentence report, and he submitted this motion to reconsider on December 10, 2001, a week after he had been sentenced. The court denied his objection, and he now renews it before this court.
This court reviews de novo the legal question of whether an information satisfied § 851. United States v. King, 127 F.3d 483, 487 (6th Cir.1997).
As stated above, to satisfy due process requirements under 21 U.S.C. § 851, the government need only (1) file an information with the court and (2) serve a copy of such information on the defendant. The information must be in writing, and both the filing and the serving must occur “before trial, or before entry of a plea of guilty.” Id.
In this case, it is undisputed that the AUSA properly filed an Information with the court on February 26, 2001, about two months before trial, to seek a statutorily enhanced sentence against Rosenboro. Therefore, the government met the first requirement.
As for the service requirement, the AUSA certified “that a true copy of the foregoing [Information was] placed in the United States Mail, postage prepaid, to” Rosenboro’s counsel on February 26, 2001. According to Fed.R.Crim.P. 49(b), “[s]er-vice upon the attorney or upon a party shall be made in the manner provided in civil actions.” Service in civil actions is governed by Fed.R.Civ.P. 5(b), which in February 2001 provided as follows, in relevant part:
Service upon the attorney or upon a party shall be made by delivering a copy to the attorney or party or mailing it to the attorney or party at the attorney’s or party’s last known address, or, if no address is known, by leaving it with the clerk of the court.... Service by mail is complete upon mailing.
Fed.R.Civ.P. 5(b) (2000) (emphasis added); see also United States v. Severino, 316 F.3d 939, 945 (9th Cir.2003) (en banc) (looking to Fed.R.Crim.P. 49(b) and Fed. R.Civ.P. 5(b) to determine whether the government had formally complied with the notice requirements of § 851(a)); United States v. Novaton, 271 F.3d 968, 1015-16 (11th Cir.2001) (same); United States v. Kennedy, 133 F.3d 53, 59 (D.C.Cir.1998) (same).
Since, according to Fed.R.Civ.P. 5(b), “[s]ervice by mail is complete upon mail[507]*507ing,” it is clear that the government also met the second requirement under § 851.4 See Severino, 816 F.3d at 945 (joining two other circuits in holding that § 851(a) service is complete upon mailing). Because the government has complied with both procedural requirements under 21 U.S.C. § 851 in seeking an enhanced sentence against Rosenboro, Rosenboro’s claims with respect to this matter are without merit.
IV.
Having found each of Appellants’ contentions without merit, we AFFIRM the judgment of the district court on all grounds.