Genomic intervals that contain a cluster of similar genes are of extreme biological interest, but difficult to sequence and analyze. One goal for interspecies comparisons of such intervals is to reconstruct a parsimonious series of duplications, deletions, and speciation events (a putative evolutionary history) that could have created the contemporary clusters from their last common ancestor. We describe a new method for reconstructing such an evolutionary scenario for a given set of intervals from present-day genomes, based on the statistical technique of Sequential Importance Sampling. An implementation of the method is evaluated using (1) artificial datasets generated by simulating the operations of duplication, deletion, and speciation starting with featureless "ancestral" sequences, and (2) by comparing the inferred evolutionary history of the amino-acid sequences for the CYP2 gene family from human chromosome 19, chimpanzee, orangutan, rhesus macaque, and dog, as computed by a standard phylogenetic-tree reconstruction method.