Understanding how and why rates of character evolution vary across the Tree of Life is central to many evolutionary questions; e.g., does the trophic apparatus (a set of continuous characters) evolve at a higher rate in fish lineages that dwell in reef versus non-reef habitats (a discrete character)? Existing approaches for inferring the relationship between a discrete character and rates of continuous-character evolution rely on comparing a null model (in which rates of continuous-character evolution are constant across lineages) to an alternative model (in which rates of continuous-character evolution depend on the state of the discrete character under consideration). However, these approaches are susceptible to a "straw-man" effect: the influence of the discrete character is inflated because the null model is extremely unrealistic. Here, we describe MuSSCRat, a Bayesian approach for inferring the impact of a discrete trait on rates of continuous-character evolution in the presence of alternative sources of rate variation ("background-rate variation"). We demonstrate by simulation that our method is able to reliably infer the degree of state-dependent rate variation, and show that ignoring background-rate variation leads to biased inferences regarding the degree of state-dependent rate variation in grunts (the fish group Haemulidae).