Methods that use outgroups in the reconstruction of phylogeny are described and evaluated by the criterion of parsimony. By considering the character states and relationships of outgroups, one can estimate the states ancestral for a study group or ingroup, even when several character states are found among the outgroups. Algorithms and rules are presented that find the most parsimonious estimates of ancestral states for binary and multistate characters when outgroup relationships are well resolved. Other rules indicate the extent to which uncertainty about outgroup relationships leads to uncertainty about the ancestral states. The algorithms and rules are based on “simple parsimony” in that convergences and reversals are counted equally. After parsimony is measured locally among the outgroups to estimate ancestral states, parsimony is measured locally within the ingroup, given the ancestral states, to find …