Abstract—The performance of four computer programs that calculate Wagner trees (WAGNER 78, WAGPROC, PHYLIP, and PHYSYS) was compared for twenty‐five data sets. Eight combinations of algorithms and options were tried, including different methods of adding taxa, optimizing stem states, obtaining multiple trees, and branch swapping. Using the criterion of finding a minimum length tree, PHYSYS with the WAG.S option performed best, providing the shortest tree for twenty‐four of the twenty‐five data sets. WAGPROC with the GLOB option found sixteen minima for eighteen data sets, exceeding run time on the remaining seven. All other algorithm/options were less successful in providing minimum trees. In comparing the options we found that minimum homoplasy is not completely reliable in optimizing trees and that the brute force algorithm is helpful but not required for finding minimum trees. The advancement index criterion for adding taxa to a tree is more effective than adding taxa in their data file sequence. The success of the PHYSYS WAG.S option and the WAGPROC GLOB demonstrate that both multiple trees and branch swapping are necessary to produce a minimum leng