The results of the study indicate that there can be relevant information in cases of unconfirmed paternity, and that excluding these, as has generally been done, can lead to biased conclusions. Taken into account were a number of sources of potential bias, including hidden mutation, incomplete family triplets, uncertain paternity status, and differing maternal and paternal mutation rates, while allowing for a wide variety of mutation models. DNA testing is often conducted to resolve a disputed attribution of paternity. However, when this results in an incompatibility (values of a child’s genotype and those of its presumed parents at some forensic marker locus that appear inconsistent with simple genetic segregation), the obvious interpretation of this is that it is due to non-paternity; an alternative possibility exists that it is, in fact, due to mutation. The DNA STR markers used for forensic purposes are particularly prone to mutation. Data on inter-allelic mutational transitions are very sparse since, in the datasets collected at forensic laboratories and used to assess mutation rates, the number of meioses where mutation appears plausible is typically very small. In order to have any chance of estimating allele-specific mutation rates from such data, models must be constructed, expressing them in terms of a small number of parameters. The main thrust of this work estimates such mutational parameters, and the overall mutation rate. A dataset from actual paternity casework was used to illustrate the effects on inferences about mutation parameters of various types of biases, and the mutation model assumed. Tables, figures, references