These appeals are brought by Blanche Elizabeth Dyer (Blanche) and Cephus Donald Dyer (Cephus), husband and wife, from drug-related convictions. The sentences as well as the convictions are attacked on appeal. After carefully considering all of the appellants' arguments, we affirm.

Blanche stands convicted of one count of conspiracy to distribute heroin and cocaine in violation of 21 U.S.C. Sec. 846; 14 counts of using communications facilities in connection with the conspiracy, in violation of 21 U.S.C. Sec. 843(b) and (c); and one count of distributing eight ounces of cocaine, in violation of 21 U.S.C. Sec. 841(a)(1) and (b)(1)(C). The District Court1 sentenced her to 230 months on count 1 and 96 months on each of the other counts of conviction, the 96-month sentence to run concurrently. A special assessment of $800 was also imposed.

Cephus was convicted of one count of conspiracy to distribute heroin and cocaine, three counts of using communications facilities in connection with the conspiracy, and one count of possession of eight ounces of cocaine with intent to distribute it. He was sentenced to 230 months on count 1 and to 48 months on each of the other four counts, the 48-month period to run concurrently. A special assessment of $250 ($50 per count, just as in Blanche's case) was imposed.

Cephus argues that the evidence was legally insufficient to support his convictions. In considering this contention, we of course apply the familiar standard: the evidence must be considered in the light most favorable to the government, and it must be given the benefit of all reasonable inferences. Only if, according to this exacting standard, a rational jury could not have found all of the elements of the offense beyond a reasonable doubt, can the appellant's contention be sustained. No purpose is to be served by recounting the evidence in detail. We have considered the entire transcript of the trial and are convinced that the evidence was sufficient to authorize the jury's conclusions.

Arguments made by both defendants with respect to their sentences deserve a somewhat fuller discussion. First, Blanche and Cephus both argue that they were deprived of liberty without due process of law when the District Court declined to use a reasonable-doubt standard in making its findings of fact after the sentencing hearing. The Sentencing Guidelines, defendants contend, are unconstitutional on their face because they fail to specify any particular burden of proof for findings of fact relevant to sentencing, let alone a reasonable-doubt burden of proof. It is true that neither the Sentencing Guidelines nor the Sentencing Reform Act that authorized them specifies a particular burden of proof for sentencing proceedings. The proper burden, however, need not be actually specified by statute. It can be supplied by decisional law, just as it has been on the question of guilt or innocence. We do not believe that a reasonable-doubt standard is required by the Constitution, and we reject appellants' argument to this effect. The ordinary, familiar preponderance-of-the-evidence standard is constitutionally sufficient. This is the standard customarily applied in sentencing proceedings, see United States v. McDowell, 888 F.2d 285 (3d Cir.1989); United States v. Urrego-Linares, 879 F.2d 1234 (4th Cir.1989); United States v. Wright, 873 F.2d 437 (1st Cir.1989). We also have referred approvingly to this standard in Sentencing Guidelines cases, see United States v. Streeter, 907 F.2d 781, 791-792 (8th Cir.1990); United States v. Gooden, 892 F.2d 725, 728 (8th Cir.1989), cert. denied, --- U.S. ----, 110 S. Ct. 2594, 110 L. Ed. 2d 274 (1990), and the Supreme Court has held that such a standard does not violate due process. McMillan v. Pennsylvania, 477 U.S. 79, 106 S. Ct. 2411, 91 L. Ed. 2d 67 (1986).

In this case the District Court made the following statement on the subject of burden of proof:

The Court will not apply any particular traditional civil measure of proof in this case because the Court believes the appropriate standard is simply to consider and give weight to reliable evidence and require proof to a reasonable certainty.

Sent. Tr. 6. The "proof to a reasonable certainty" standard is, in our view, the functional equivalent of a preponderance-of-the-evidence standard, and certainly no less favorable to defendants than such a standard. We therefore see no error of law prejudicial to defendants' substantial rights in the method used by the District Court to make its findings in this case.

Cephus also argues that it was error to classify him as a career offender. This finding by the District Court resulted in an offense level of 32, which, when combined with a criminal history category of VI, produced a Guideline range for Cephus of 210 to 262 months. The sentence actually imposed, 230 months, falls approximately in the middle of this range. The career-offender finding, which is a key element in the calculation of Cephus's sentence, depends for its validity on the Court's subsidiary findings as to various prior convictions that Cephus had sustained, including a 1970 conviction for robbery, a 1974 conviction for robbery, and a 1974 conviction for kidnapping. The governing provision of the Guidelines is Sec. 4B1.1, under which "two prior felony convictions of either a crime of violence or a controlled substance offense" are required. The crime-of-violence requirement is clearly met, but Cephus contends that the 1970 conviction is too old to be counted, and that the 1974 robbery and kidnapping convictions were related offenses and therefore should count as only one. The language of S.G. Sec. 4A1.2(e)(1) refutes this contention. Under this provision, the sentencing court is to count "any prior sentence of imprisonment exceeding one year and one month that resulted in the defendant's incarceration during any part of such 15 year period." The 15-year period referred to is the 15 years ending with the defendant's commencement of the instant offense. The 1970 robbery conviction resulted in a sentence of seven years' imprisonment, of which Cephus served three years and ten months. He was incarcerated until December 1973. The instant offense commenced before December 1988, and therefore the 1970 robbery conviction qualifies for career-offender-counting purposes. Accordingly, even if the 1974 robbery and kidnapping convictions are related, so as to count for only one, the requirement of two prior violent offenses is met, and the District Court did not err in classifying Cephus as a career offender.2

Blanche argues that it was improper to give her a two-point enhancement under Sec. 3C1.1, which has to do with impeding or obstructing the administration of justice during the investigation or prosecution. Blanche freely admitted her own crimes on the witness stand, but she testified that Cephus had nothing to do with them, and the District Court found that this was a lie. This finding is not clearly erroneous. Perjury at trial unquestionably amounts to obstruction of justice within the meaning of Sec. 3C1.1. There was no error in applying this two-point enhancement. In the circumstances of this case, it necessarily follows that it was not error to deny Blanche a two-level reduction for acceptance of responsibility. In assessing whether this reduction should have been granted, we give great deference to the sentencing judge. E.g., United States v. Nunley, 873 F.2d 182 (8th Cir.1989). Blanche's perjury on the witness stand at trial, which was not itself followed by any signs of repentance or remorse, is fully sufficient to justify the District Court's action in refusing the two-level reduction for acceptance of responsibility. There was no error in this respect.

Finally, Blanche argues that she should not have been given a four-level enhancement for being a leader or organizer in a criminal enterprise involving five or more people. The applicable provision of the Guidelines is Sec. 3B1.1(a). The District Court found that seven persons were involved in this criminal activity, the two defendants, Joni Kay Lewis, Marshall Gatton, Patricia Epperson, and two unnamed persons who sold drugs to members of the conspiracy. Blanche argues that Marshall Gatton cannot be counted because he was a government informant, and that persons who merely sell drugs to members of the conspiracy are not sufficiently closely connected to count as participants in the enterprise. Even if all of these arguments are accepted, Blanche's position on this point cannot succeed: evidence at trial indicated that Gatton was part of the drug dealings before becoming a government informant. The District Court was justified in treating Gatton as one of the five (at least) participants for Guidelines purposes.

We have carefully reviewed the pro se supplemental briefing of Cephus and Blanche. Their various assertions of error in the trial below are without merit. Cephus argues that he received ineffective assistance of counsel at his trial. Because this claim was not raised before the District Court, we do not address it at this level. Cephus also claims his offense level of 32 erroneously includes a two-level increase for use of a firearm. It plainly does not, for reasons already discussed. And the government did prove sufficiently that Cephus was involved in the conspiracy to supply drugs to Epperson, thus United States v. North, 900 F.2d 131 (8th Cir.1990), does not require reversal of his conviction.

Having fully reviewed all of defendants' arguments, we conclude that the judgments and sentences must be

Affirmed.