Abstract—Objections to my earlier demonstration, that the branch lengths of trees fitted to distance matrices have no physical interpretation, are shown to be ill‐founded. In particular the contention of Felsenstein, that fitted lengths estimate expectations of amounts of change, is shown to lead to a paradox. A method is introduced for constructing multiple trees of optimal or near‐optimal fit to distance data, and this is found to give better performance than previous methods. Most published trees based on distances have been poorly chosen. Consensus trees of several trees with near‐optimal fit are found to be quite poorly resolved, and it appears that molecular distances seldom provide much useful information on phylogenetic relati