The bootstrap computer-intensive statistical technique is frequently applied to statistical analyses of phylogenetic trees. The widely used rule that a group is supported significantly if it appears in at least 95% of bootstrap trees is conservative in most situations. This paper describes three ways of using the bootstrap to carry out statistical inference on phylogenies. The first method tests whether there is nonrandom support for a single group or tree. The second method compares the support for two groups or trees. The third method tests whether a single group or tree has better support than the set of all possible alternatives; this may be a replacement for the "95% rule." These tests generally require fewer bootstrap trees to be estimated than do other methods of bootstrapping phylogenies. A simple, sequential statistical method can be used to increase the efficiency further. These methods can be applied to tests of multiple hypotheses about a single phylogeny. Parsimony analyses of 5S rRNA sequences of plants and cluster analyses of randomly amplified polymorphic DNA bands in three pathotypes of the cereal eyespot fungus are used as illustrative examples. The tests can be used to analyze dendrograms in subjects other than taxonomy.