?Discriminate compatibility measures are introduced. The character discriminate compatibility and the average character discriminate compatibility measures are used in weighted parsimony analysis in an iterative procedure, the reduction routine, to build trees. The data set discriminate compatibility measure is used to order and polarize characters. The average data set discriminate compatibility measure is used to measure the fit of different data sets and different user trees. Three inadequacies in the Le Quesne compatibility tests (Le Quesne, 1969, Syst. Zool. 18:201-205; 1979, Syst. Zool. 28:92-94) as applied by Penny and Hendy (1985, Cladistics 1:266272; 1986, Mol. Biol. Evol. 3:403-417) and Sharkey (1989, Cladistics 5:63-86) are discussed. [Char? acter weighting; cladistics; compatibility; congruence; consistency index; phylogeny.] The importance, for classification, of trifling char? acters, mainly depends on their being correlated with many other characters. ?Charles Darwin, 1859:417 The more correlated a character state is with respect to other character states, the more one may be convinced that it is a synapomorphy. As indicated by the quo? tation from Darwin, the criterion of cor? relation has been an intuitive method of character evaluation for almost 150 years. In the present paper, I attempt to quantify this thinking to obtain an objective, ra? tional, and repeatable method of phylo? genetic reconstruction. There are two basic types of character correlation. When characters are correlated with respect to a phylogenetic hypothesis, they are termed congruent with the hy? pothesis. When characters are correlated with each other in the data set, they are termed compatible. Farris (1971) made these distinctions clear. Compatibility (a form of which is used here) is an a priori concept of correlation, whereas congruence is an a posteriori notion. The two most fundamental questions to be addressed in this paper are how does one measure compatibility, and how is this 1 E-mail: sharkeym@ncccot2.agr.ca. measure employed to obtain hypotheses of phylogenetic relationship? A priori assumptions of the method de? scribed here are that there are two reasons for character compatibility, i.e., phylogeny and chance. At least in part, homoplastic characters may be compatible with synapomorphies and with other homoplastic characters by chance. When choosing be? tween two incompatible characters (one of which must be homoplastic), the character with a distribution most likely to be the product of chance should be rejected in favor of that with a distribution that is un? likely to be the result of chance. Le Quesne (1979) presented a method for measuring the reliability of polarized data that was derived from a method for un? polarized data from an earlier paper (Le Quesne, 1969). In these papers, Le Quesne treat d each occurrence of a character in? dependently such that each character was hypothesized to be a collection of random events. The method proposed here also uses this model of randomness. As pointed out by Farris (1977:79-80), this model of ran? domness does not accurately reflect the properties of homoplastic characters. If the assumptions of randomness and indepen? dence made by Le Quesne were fully justified for all characters, there would be little point in at? tempting phylogenetic analysis, for these assump? tions effectively exclude the possibility of any tax-