In this paper, we describe a method for the inference of gene family members from unassembled sequencing traces. The method is conceptually straightforward, and is based on an information-theoretic model that accounts for both sequencing error and evolutionary divergence, providing the means to encode the set of sequencing traces. We then seek those partial assemblies that make the total description length of the combined set of sequencing traces as small as possible. This reconstruction provides an estimate of the number of genes in the family and posterior probability mass functions on the DNA sequences of these genes.