A new statistical model for DNA considers a sequence to be a mixture of regions with little structure and regions that are approximate repeats of other subsequences, i.e. instances of repeats do not need to match each other exactly. Both forward-and reverse-complementary repeats are allowed. The model has a small number of parameters which are fitted to the data. In general there are many explanations for a given sequence and how to compute the total probability of the data given the model is shown. Computer algorithms are described for these tasks. The model can be used to compute the information content of a sequence, either in total or base by base. This amounts to looking at sequences from a data-compression point of view and it is argued that this is a good way to tackle intelligent sequence analysis in general.