The abundance of cosmological data becoming available means that a wider range of cosmological models are testable than ever before. However, an important distinction must be made between parameter fitting and model selection. While parameter fitting simply determines how well a model fits the data, model selection statistics, such as the Bayesian evidence, are now necessary to choose between these different models, and in particular to assess the need for new parameters. We implement a new evidence algorithm known as nested sampling, which combines accuracy, generality of application, and computational feasibility, and we apply it to some cosmological data sets and models. We find that a five-parameter model with a Harrison-Zel'dovich initial spectrum is currently preferred.