Dynamic cognitive psychometrics measures mental capacities based on the way behavior unfolds over time. It does so using models of psychological processes whose validity is grounded in research from experimental psychology and the neurosciences. However, these models can sometimes have undesirable measurement properties. We propose a “hybrid” modeling approach that achieves good measurement by blending process-based and descriptive components. We demonstrate the utility of this approach in the stop-signal paradigm, in which participants make a series of speeded choices, but occasionally are required to withhold their response when a “stop signal” occurs. The stop-signal paradigm is widely used to measure response inhibition based on a modeling framework that assumes a race between processes triggered by the choice and the stop stimuli. However, the key index of inhibition, the latency of the stop process (i.e., stop-signal reaction time), is not directly observable, and is poorly estimated when the choice and the stop runners are both modeled by psychologically realistic evidence-accumulation processes. We show that using a descriptive account of the stop process, while retaining a realistic account of the choice process, simultaneously enables good measurement of both stop-signal reaction time and the psychological factors that determine choice behavior. We show that this approach, when combined with hierarchical Bayesian estimation, is effective even in a complex choice task that requires participants to perform only a relatively modest number of test trials.