We describe an approach to analyzing protein sequence databases that, starting from a single uncharacterized sequence or group of related sequences, generates blocks of conserved segments. The procedure involves iterative database scans with an evolving position-dependent weight matrix constructed from a coevolving set of aligned conserved segments. For each iteration, the expected distribution of matrix scores under a random model is used to set a cutoff score for the inclusion of a segment in the next iteration. This cutoff may be calculated to allow the chance inclusion of either a fixed number or a fixed proportion of false positive segments. With sufficiently high cutoff scores, the procedure converged for all alignment blocks studied, with varying numbers of iterations required. Different methods for calculating weight matrices from alignment blocks were compared. The most effective of those tested was a logarithm-of-odds, Bayesian-based approach that used prior residue probabilities calculated from a mixture of Dirichlet distributions. The procedure described was used to detect novel conserved motifs of potential biological importance.