Random sampling of paid Medicare claims is a legally acceptable approach for investigating suspicious billing practices by supposed health care providers. A population of payments made to a given provider during a given time frame is identified, and a probability sample selected for investigation. For each claim, the overpayment is defined to be the amount paid minus the amount that should have been paid given the evidence. Using the sample of overpayments, a nominal 95% lower confidence bound for the total overpayment over the entire population is computed and used as a recoupment demand to the provider. It is not unusual for these recoupment demands to exceed a million dollars. Though they are conservative in most settings, for certain kinds of overpayment populations the standard methods for confidence bounds based on the Central Limit Theorem can fail badly. Here, we develop "nonparametric sampling" inferential methods for simple random samples based on the Hypergeometric distribution, and study their performance on real payment populations. They are found to provide more than the nominal coverage probability at any sample size, and to be surprisingly efficient relative to the Central Limit Theorem bounds for payment populations whose values are well-separated from zero.