Partial restriction digestion is used to map restriction sites and the location of genes within yeast artificial chromosomes (YACs). Locus-specific probes are hybridised to the partially digested YAC DNA and the fragments to which they hybridise are compared with the pattern of partial digestion products that include each map region. A least squares criterion is presented which allows for error in fragment length determination. This rapidly defines the most likely location of a marker within the restriction map and permits the combination of results from digestions with different restriction enzymes. Approximate confidence intervals may be assigned to gene locations, and tests of goodness-of-fit of the data may be performed. Since the number of erroneously matched fragments increases in proportion to the square of the number of sites, denser maps are not necessarily more informative. Simulations indicate that the optimal number of internal restriction sites given typical experimental error (1% of YAC length) is about five sites; the associated broad support interval (on average one third of YAC length) may be reduced by combining results from different enzyme digestions. Application of a computer implementation of this model to experimental data showed that the model fitted well, and estimates of location were found to be consistent with other evidence.