PER CURIAM.

This case returns to us following our remand to the District Court for further review of two issues. In United States v. Rushing, 313 F.3d 428 (8th Cir. 2002), we asked the District Court to determine whether certain expert testimony, excluded at trial, was properly excluded under Daubert v. Merrell Dow Pharm., 509 U.S. 579, 113 S.Ct. 2786, 125 L.Ed.2d 469 (1993), and Fed.R.Evid. 702. Second, we asked the District Court to explore the defendants' allegation that the prosecution violated Brady v. Maryland, 373 U.S. 83, 83 S.Ct. 1194, 10 L.Ed.2d 215 (1963), and Giglio v. United States, 405 U.S. 150, 92 S.Ct. 763, 31 L.Ed.2d 104 (1972), by withholding evidence of an agreement with a government witness. After considering these issues, the District Court certified its findings and conclusions to this Court for review, and we affirm.

The issues presented stem from the defendants' convictions of various offenses involving the immigration of two Chinese women into the United States. The prosecution's case at trial was built on the theory that the defendants — David Jewell Jones, Tony Ma, and Bob Rushing — illegally assisted the women in entering this country so that Mr. Jones could engage in sexual relations with them. At trial one of the women, Ms. Zhong, testified for the government about her sexual relationship with Mr. Jones. A more complete statement of the facts of this case can be found in our previous opinion, Rushing, 313 F.3d at 429-32. It is important to keep in mind that the crimes charged had to do with immigration fraud — whether defendants conspired with each other to make false statements to assist the entry of the two women into the United States.

I.

We first examine the issue of whether the testimony of the defendants' expert witness was properly excluded at trial. Ms. Zhong testified that she and Mr. Jones had sexual intercourse about once a week over a time period of approximately one year. The defense refuted Ms. Zhong's claim, asserting that Mr. Jones was incapable of sexual relations because he is impotent. The defendants also sought to discredit Ms. Zhong through the testimony of an expert witness, Paul Gubbins, who holds a Doctor of Pharmacy degree.

The proffered testimony of Dr. Gubbins was essentially that the medical histories of Ms. Zhong and Mr. Jones indicated that they did not engage in a sexual relationship as described by Ms. Zhong. Dr. Gubbins would have testified that Ms. Zhong was infected with Hepatitis B and that, due to the prevalence of this disease in China, she was most likely infected at the time she entered this country. According to Dr. Gubbins, if Ms. Zhong and Mr. Jones had engaged in a year-long sexual relationship, then, more likely than not, Mr. Jones would have contracted Hepatitis B. Because Mr. Jones was not infected, this expert testimony would have supported the defense position that no sexual relationship occurred while undermining the prosecution's case.

The District Court excluded Dr. Gubbins's testimony based on Fed.R.Evid. 403, finding that it was collateral to the issue of whether the defendants had committed immigration fraud. Upon review of that finding we disagreed, holding that the evidence would have been highly probative, as the government alleged that Mr. Jones's sexual gratification was the defendants' motive to bring Ms. Zhong into the United States. Rushing, 313 F.3d at 434-35. The government, however, argued that Dr. Gubbins's testimony was nevertheless excludable because it was unreliable under Daubert. We therefore remanded the case so that the District Court could address the reliability issue and determine whether the evidence was properly excluded. Id. at 435.

Under Federal Rule of Evidence 702, expert testimony may be admitted only "if (1) the testimony is based on sufficient facts or data, (2) the testimony is the product of reliable principles and methods, and (3) the witness has applied the principles and methods reliably to the facts of the case." In Daubert, the Supreme Court charged trial courts with the responsibility of screening such testimony for reliability by assessing the expert's reasoning and methodology. Peitzmeier v. Hennessy Indus., Inc., 97 F.3d 293, 296-97 (8th Cir. 1996) (citing Daubert, 509 U.S. at 591-93, 113 S.Ct. 2786). Expert testimony should not be admitted when it is speculative, it is not supported by sufficient facts, or the facts of the case contradict or otherwise render the opinion unreasonable. Concord Boat Corp. v. Brunswick Corp., 207 F.3d 1039, 1056-57 (8th Cir. 2000) (citations omitted). We review the exclusion of expert testimony for an abuse of discretion. Peitzmeier, 97 F.3d at 296.

On remand, the District Court found that Dr. Gubbins's testimony was not admissible because it was not based upon sufficient facts or data, it was not the product of reliable methods, and he applied his criteria using assumptions contrary to the established facts of the case. Specifically, Dr. Gubbins admitted that in forming his opinion, he failed to take into account that there was no information about Ms. Zhong's level of infectiousness during the period of her sexual relationship with Mr. Jones; that Hepatitis B progresses differently in women than it does in men; and that it would be less likely for Mr. Jones to have acquired the disease from Ms. Zhong than it would have been for a woman from a man. Dr. Gubbins further stated that he could not say with any degree of scientific certainty that it is highly likely that a man would have contracted Hepatitis B from a woman. In addition, Dr. Gubbins stated that in forming his opinion as to the risk of infection, he assumed that Mr. Jones and Ms. Zhong had sex two to three times per week, contrary to Ms. Zhong's record testimony that she and Mr. Jones had sex about once a week.

Furthermore, the government presented its own expert witness, Harold Margolis, M.D., of the Centers for Disease Control, who disagreed with Dr. Gubbins's assessment of the risk of infection. Dr. Margolis testified that Mr. Jones had only about a ten per cent. chance of infection over the course of a year. While the fact that the government would have presented an opposing expert is not by itself a sufficient reason to exclude Dr. Gubbins's testimony, it was a factor that the District Court properly considered in its assessment. See Daubert, 509 U.S. at 580, 113 S.Ct. 2786 (holding that a federal court's inquiry into the reliability of expert testimony is flexible and may depend upon a variety of considerations). The District Court's analysis and findings as to this issue are extensive and well-reasoned. We see no abuse of discretion in its conclusion that the defendants' proffered expert testimony was unreliable and thus inadmissible.

II.

We now address the defendants' contention that the prosecution violated Brady and Giglio by withholding evidence of an agreement with a government witness. The backdrop of events relevant to this issue takes us back to Ms. Zhong's involvement with Mr. Jones.

Ms. Zhong initially reported, in statements to law-enforcement officers and the Immigration and Naturalization Service (INS), that Mr. Jones had raped her. She later changed her story, admitting that their sexual relationship was consensual. Consequently, Ms. Zhong was indicted on March 7, 2001, for making a false statement to law-enforcement officers. In May of 2001, Ms. Zhong was compelled to testify, under a grant of use immunity, about her sexual relationship with Mr. Jones at his trial for immigration fraud. During the trial, an Assistant United States Attorney told the jury that Ms. Zhong would be prosecuted for her prior false statements, imprisoned, and then deported. Ms. Zhong also testified that she understood that the government intended to deport her. Mr. Jones was then convicted.

After the Jones trial, Ms. Zhong eventually pleaded guilty to the false-statement charge. The plea agreement provided that the government would recommend leniency in sentencing and that, if Ms. Zhong sought relief from deportation through asylum, the U.S. Attorney would inform the presiding judge that Ms. Zhong cooperated with the government in connection with another case. This situation seemed to be a change of position by the government with no obvious explanation.

The defendants now claim that before the Jones trial the prosecution had actually made an agreement with Ms. Zhong not to deport her in exchange for her testimony, and then intentionally concealed that agreement. At trial, Ms. Zhong's credibility was central to the government's case. If she were testifying against Mr. Jones in exchange for leniency, the defense would be entitled to this information and the opportunity to cross-examine her. The defendants' charge is thus quite serious, as such misconduct would not only run afoul of Brady and Giglio, but would be a gross ethical violation as well.

The government has a duty to disclose to a defendant any evidence in its possession that is material and favorable to the defense. Brady, 373 U.S. at 87, 83 S.Ct. 1194. In Giglio, the Supreme Court extended this responsibility, requiring disclosure of agreements or understandings between the government and a witness for leniency in exchange for testimony. Giglio, 405 U.S. at 154-55, 92 S.Ct. 763. These rules are designed to protect a defendant's fundamental right to fairness under the Due Process Clause of the Fifth Amendment, for when the fate of the accused turns on the credibility of a witness, the prosecutor's failure to disclose a potential motive for bias or untruthfulness may result in grave injustice. The government's apparent change of position regarding Ms. Zhong's prosecution and deportation after the trial concerned us and prompted our remand of the issue to the District Court for further exploration. See Rushing, 313 F.3d at 436.

We review a District Court's factual findings for clear error. United States v. Williams, 346 F.3d 796, 798 (8th Cir. 2003). On remand, the District Court found that before the Jones trial the prosecution did make an offer to Ms. Zhong for leniency if Ms. Zhong would cooperate with the prosecution. Ms. Zhong rejected that offer, however, and no plea agreement was reached. Giglio does not require disclosure of rejected plea offers; the duty to disclose is dependent upon the existence of an agreement between the witness and the government. Collier v. Davis, 301 F.3d 843, 849-50 (7th Cir. 2002); Alderman v. Zant, 22 F.3d 1541, 1555 (11th Cir. 1994). Thus, when Ms. Zhong testified against Mr. Jones, no plea agreement was in place, and the government had no duty to disclose the rejected offer.

Further, the District Court found that the government continued its efforts to prosecute Ms. Zhong after the Jones trial. In September 2001, the government reached its plea agreement with Ms. Zhong. At that point, the government had reached the conclusion that, under the United States Sentencing Guidelines, Ms. Zhong would not be subject to incarceration whether she pleaded guilty or went to trial. Thus, while she was sentenced to one year of probation, not incarceration, this sentence reflected the range set forth by the Sentencing Guidelines, not a prosecutorial decision to show Ms. Zhong leniency.

Finally, the plea agreement provided that if Ms. Zhong chose to seek relief from deportation by applying for asylum, the government would advise the presiding judge that she had testified for the government in Mitchell for whatever value that court would give it. The important point here is that the government did not change its position regarding Ms. Zhong's deportation. The government consistently maintained that she should be deported and initiated deportation proceedings against her. The Assistant United States Attorney anticipated, however, that Ms. Zhong would seek relief in the form of asylum and thus agreed to advise the judge in the asylum proceedings that Ms. Zhong had provided some assistance to the government in the Mitchell case. Because her testimony in Mitchell was a matter of public record, this information could have been presented to the presiding judge in any event — the U.S. Attorney's minimal assistance to Ms. Zhong on this point was simply a matter of basic fairness to her. Moreover, while the U.S. Attorney prosecuted Ms. Zhong and moved to deport her, the final decision to deport her or grant her asylum rested with the United States Immigration and Customs Enforcement, a separate governmental agency. In sum, there is no evidence that the assistant U.S. Attorney involved in this case made any sort of undisclosed agreement with Ms. Zhong to secure her testimony against Mr. Jones or otherwise acted in bad faith.

For the reasons stated herein, we affirm the judgment of the District Court.

III.

In our original decision in this case, we reserved for later determination sentencing issues raised by Mr. Jones in his appeal and in a cross appeal by the government. We indicated that we would decide those sentencing issues if the convictions in this case were ultimately affirmed. Since we are now affirming the convictions, we need to decide those sentencing issues.

We have carefully considered each of the issues raised by the parties and find no error by the district court. We do not believe that an extended discussion of the sentencing issues is necessary and summarily affirm. See 8th Cir. Rule 47B.