Interpreting a taxonomic tree as a set of objects leads to natural measures of complexity and similarity, and sets natural lower bounds on a consensus tree Interpretations differing as to the kind of objects constituting a tree lead to different measures and consensus Subset nesting is preferred over the clusters (strict consensus) and even the triads interpretations because of its superior expression of shared structure Algorithms for computing the complexity and similarity of trees, as well as a consensus index onto [0,1], are presented for this interpretation The “full consensus” is defined as the only tree which includes all the nestings shared in a profile of rival trees and whose clusters reflect only nestings shared in the profile The full consensus is proved to exist uniquely for each profile, and to equal the Adams consensus