We examine the use of internal controls for estimating the expected initial copy number of the target in a polymerase chain reaction (PCR). We base our investigation on an extended branching-process model. In terms of that model, we delineate the necessary assumptions for this methodology to yield approximately unbiased answers, and we provide means for testing some of those assumptions. We show how to design a series of PCRs to attain optimal precision of the estimate. We provide an algorithm for conducting the statistical analysis of the data, including a formula for a confidence interval for the unknown expected initial copy number.