Rates of molecular evolution vary substantially between lineages, and a growing research effort is directed at uncovering the causes and consequences of this variation. Comparing local-clocks (rates of molecular evolution estimated from sets of branches of a phylogenetic tree) is a common tool in this research effort. Here, I show that a commonly used test (the Likelihood Ratio Test, LRT) will not be statistically valid for comparing local-clocks in most cases. Instead, I propose the local-clock permutation test (LCPT), a simple test which can be used to test the significance of differences between local-clocks. The LCPT could also be used to test for differences between any parameter that can be assigned to individual branches on a phylogenetic tree. Using simulated data, I show that the LCPT has good power to detect differences between local-clocks.