1. Understanding variation in rates of speciation and extinction -- both among lineages and through time -- is critical to the testing of many hypotheses about macroevolutionary processes. BAMM is a flexible Bayesian framework for inferring the number and location of shifts in macroevolutionary rate across phylogenetic trees and has been widely used in empirical studies. BAMM requires that researchers specify a prior probability distribution on the number of diversification rate shifts before conducting an analysis. The consequences of this "model prior" for inference are poorly known but could potentially influence both the probability of accepting models that are more (high error rate) or less (low power) complex than the generating model. 2. The hierarchical Poisson process prior in BAMM reduces to a simple geometric distribution on number of rate shifts and we use this property to increase the efficiency of model selection with Bayes factors. Using BAMM v2.5, we analyzed phylogenies simulated with and without diversification heterogeneity across a broad range of prior parameterizations. We also assessed the impact of the model prior on MCMC convergence times and on diversification rate estimates. 3. For all simulation scenarios, model evidence (Bayes factor support) for the number of shifts is not sensitive to the choice of model prior over the wide range examined here. The best-supported model found using BAMM rarely includes spurious shifts (<2% of all runs) when diversification models are selected using Bayes factors. BAMM was reliably able to infer the true number of diversification rate shifts across prior expectations that varied by three orders of magnitude. However, we find a strong effect of model prior on MCMC convergence properties: a flatter prior distribution (larger expected number of shifts) can dramatically increase the efficiency of the MCMC simulation. 4. Our results support the use of a liberal model prior in BAMM, as it reduces computation time without distorting the evidence for rate heterogeneity.