Consensus trees are required to summarise trees obtained through MCMC sampling of a posterior distribution, providing an overview of the distribution of estimated parameters such as topology, branch lengths and divergence times. Numerous consensus tree construction methods are available, each presenting a different interpretation of the tree sample. The rise of morphological clock and sampled-ancestor methods of divergence time estimation, in which times and topology are co-estimated, has increased the popularity of the maximum clade credibility (MCC) consensus tree method. The MCC method assumes that the sampled, fully resolved topology with the highest clade credibility contains an adequate summary of the most probable clades, with parameter estimates from compatible sampled trees used to obtain the marginal distributions of parameters such as clade ages and branch lengths. Using both simulated and empirical data, we demonstrate that MCC trees, and trees constructed using the similar maximum a posteriori (MAP) method, often include poorly supported and incorrect clades when summarising diffuse posterior samples of trees. We demonstrate that the paucity of information in morphological datasets contributes to the inability of MCC and MAP trees to present an accurate summary of the posterior distribution. Conversely, majority-rule consensus (MRC) trees report a lower proportion of incorrect nodes when summarising the same posterior samples of trees. Thus, we advocate the use of MRC trees, in place of MCC or MAP trees, in attempts to summarise the results of Bayesian phylogenetic analyses of morphological data.