The distribution of diversity can vary considerably from clade to clade. Attempts to understand these patterns often employ state speciation and extinction models to determine whether the evolution of a particular novel trait has increased speciation rates and/or decreased their extinction rates. It is still unclear, however, whether these models are uncovering important drivers of diversification, or whether they are simply pointing to more complex patterns involving many unmeasured and co-distributed factors. Here we describe an extension to the popular state speciation and extinction models that specifically accounts for the presence of unmeasured factors that could impact diversification rates estimated for the states of any observed trait. Specifically, our model, which we refer to as HiSSE (Hidden State Speciation and Extinction), assumes that related to each observed state in the model are “hidden” states that exhibit potentially distinct diversification dynamics and transition rates than the observed states in isolation. Under rigorous simulation tests and when applied to empirical data, we find that HiSSE performs reasonably well, and can at least detect net diversification rate differences between observed and hidden states. We also discuss the remaining issues with state speciation and extinction models in general, and the important ways in which HiSSE provides a more nuanced understanding of trait-dependent diversification.