Recombinant inbred (RI) strains are useful in linkage analysis and gene mapping. However, the generally small number of strains in an RI strain set limits the power of RI strains in linkage detection. Several methods for increasing the power of RI strains have been used, including summing data across RI strain sets and excluding linkage to genomic regions. In this paper, Bayesian analysis is applied to three-locus linkage data. This method further increases the power of RI strains to detect linkage and gives estimations of the probability of each of the three possible gene orders if the test locus is linked to the pair of marker loci. Several examples are presented, including reconsideration of the position of the proto-oncogene L-myc on the mouse linkage map.