Two methods are proposed to find the maximum likelihood parameter estimates of a number of software reliability models. On the basis of the results from analysing 7 sets of real data, these methods are found to be both efficient and reliable.\ud \ud The simple approach of adapting software reliability predictions by Keiller and Littlewood (1984) can produce improved predictions, but at the same time, introduces a lot of internal noise into the adapted predictions. This is due to the fact that the adaptor is a joined-up function.\ud \ud An alternative adaptive procedure, which involves the parametric spline adaptor, can produce at least as good adapted predictions without the predictions being contaminated by internal noise as in the simple approach.\ud \ud Miller and Sofer (1986a) proposed a method for estimating the failure rate of a program non-parametrically. Here, these non-parametric rates are used to produce reliability predictions and their quality is analysed and compared with the parametric predictions.