A basic concern when using decision trees for the solution of taxonomic or similar problems is their efficiency. Often the information that is required to completely optimize a tree is simply not available. This is especially the case when a criterion based on probabilities is used. It is shown how it is often possible, despite the absence of this information, to improve the design of the tree. The approach is based on algebraic methods for manipulating decision trees and the identification of some particularly desirable forms.
