This article reviews objections to optimal-matching (OM) algorithms in sequence analysis and reformulates the concept of sequence similarity in terms of a binary precedence relation. This precedence relation is then used to develop a new quantification of sequence similarity. The new measure is used to reanalyze the life history data that were previously discussed by Dijkstra and Taris (1995). The reanalysis demonstrates the new measure to be superior to the OM algorithm and the alternatives proposed by Dijkstra and Taris. A new algorithm is presented to enumerate matching k-tuples from pairs of sequences in polynomial time.