?Two new optimality indices are developed for selecting subsets of trees from a set of parsimonious trees. The optimal character compatibility index (OCCI) quantifies, for each parsimonious tree, the proportion of characters that are postulated to have changed only once. The tree(s) with the highest OCCI value is (are) selected. The optimum parsimonious likelihood index (OPLI) selects the tree(s), from a set of parsimonious trees, that is (are) likely to give the observed data under certain assumptions. In simulation trials, both the OCCI and OPLI are highly efficient at retrieving the closest approximation to the true tree. [Phylogeny; parsimony; optimality criteria; maximum likelihood; compatibility.] In cladistic analysis, the phylogenetic re? lationships of operational taxonomic units (OTUs) may be estimated by using the cri? terion of maximum parsimony, in which a tree with the minimum number of char? acter transformations is taken to represent the best hypothesis of these relationships (Kluge and Farris, 1969). If all characters in a given character-OTU array are good indicators of phylogeny, the resulting minimum-length tree will have a length that is close to the total number of derived character states (i.e., the tree consistency index, as defined by Kluge and Farris, will be close to 1). However, in cases, there will be a subset of characters that is not strictly contingent on ancestry but repre? sents either adaptations or reflections of structural plasticity. Characters such as these may be incompatible (sensu Estabrook, 1984:149) with ancestrally deter? mined characters. An analysis in which these characters are used often results in a suite of parsimonious trees, each ex? hibiting some degree of homoplasy. A researcher faced with multiple parsimonious trees can do one of several things: (1) present all such trees as hy? potheses of phylogeny; (2) review all trees and select the best tree (on the basis of 1 Present address: Department of Zoology, Univer? sity of Auckland, Private Bag 92019, Auckland, New Zealand. informed speculations and a priori expec? tat ons concerning the relationships and stabilities of the characters); (3) apply some form of character weighting; (4) construct a consensus tree; or (5) use an alternative optimality criterion in addition to that of minimum length to select one or a subset of parsimonious trees. The first of these options can be used if the number of parsimonious trees is small (less than 5). However, with large sets of minimum-length trees, this option will be impractical and uninformative. Al? ternatively, a researcher may decide to pursue the second course of action and se? lect a tree on the basis of speculations about most probable relationships. In many cases, however, there is little or no prior knowledge about plausible OTU relation? ships or even about the stability of the characters used to define such relation? s ips. Character weighting procedures such s those described by Farris (1969) and Pen? ny and Hendy (1985) are certainly viable alternatives, usually reducing the number of (weighted) parsimonious trees. However, there is as yet no agreement on the merits or indeed the methods of as? signing unequal weights to characters, and many systematists treat such procedures warily. The same can be said of the use of consensus trees, particularly given the crit? icisms levelled against consensus methods (Carpenter, 1988; cf. Anderberg and Tehler, 1990). The advantage of using an al-