The Jelinski-Moranda (JM) model for software reliability growth is one of the most commonly cited (often in its guise as the `Musa model¿¿). Recent studies show that the reliability estimates and predictions given by the model are often grossly inaccurate. It has been suggested that one reason for this poor performance may be the use of the maximum-likelihood method of inference. This paper describes a Bayesian version of the model and shows that it is sometimes an improvement on JM. However, both versions have a tendency to give optimistic answers, probably owing to a key, but implausible, underlying assumption common to both models. The authors conclude that the generally poor performance of the models is such that they should only be used with great caution.