Risky intertemporal choices involve choosing between options that can differ in outcomes, their probability of receipt, and the delay until receipt. To date, there has been no attempt to systematically test, compare, and evaluate theoretical models of such choices. We contribute to theory development by generating predictions from 7 models for 3 common manipulations-magnitude, certainty, and immediacy-across 6 different types of risky intertemporal choices. Qualitative and quantitative comparisons of model predictions to data from an experiment involving almost 4,000 individual choices revealed that an attribute comparison-model, newly modified to incorporate risky intertemporal choices, (the risky intertemporal choice heuristic or RITCH) provided the best account of the data. Results are consistent with growing evidence in support of attribute comparison models in the risky and intertemporal choice literatures, and suggest that the relatively poorer fits of translation-based models reflect their inability to predict the differential impact of certainty and immediacy manipulations. Future theories of risky intertemporal choice may benefit from treating risk and time as independent dimensions, and focusing on attribute-comparison rather than value-comparison processes. (PsycInfo Database Record (c) 2020 APA, all rights reserved).