In many areas, such as reliability and forensic identification, it is of interest to estimate a product of unknown parameters, each of which is estimated from test data. The maximum likelihood estimator usually used in both applications is approximately unbiased but has an asymmetric sampling distribution, particularly when the sample size is not large. Consequently, most estimates understate the parameter value, often substantially, and this may be a serious drawback if “overoptimism” is highly undesirable. Further, widely used methods of interval estimation based on confidence limits suffer from a range of theoretical and computational problems. Alternative methods of estimation are developed and discussed, based on frequentist, Bayesian, and likelihood approaches.