A fast method for reconstructing phylogenies from distance data is presented. The method is economical in the number of pairwise comparisons needed. It can be combined with a new phylogenetic alignment procedure to yield an algorithm that gives a complete history of a set of homologous sequences. The method is applicable to very large distance matrices. An auxiliary program was developed that simplifies large phylogenies without ignoring biologically essential features. A set of 213 globins from vertebrates, plants, and Vitreoscilla (a prokaryote) were analyzed using this method.