The Bayes method of tree reconstruction is a recent major advance in molecular phylogenetics. It provides an attractive alternative to maximum likelihood with bootstrap due to the easy interpretation of posterior probabilities for trees and to availability of efficient computational algorithms. However, for many data sets it produces extremely high posterior probabilities, sometimes for apparently incorrect clades. Here we use both computer simulation and empirical data analysis to examine the effect of the prior model for branch lengths. We found that the so-called non-informative priors for branch lengths (which are nuisance parameters in the model) can produce spuriously high posterior probabilities for trees (which are the parameter of interest).