How can a task-appropriate response be selected for an ambiguous target stimulus in task-switching situations? One answer is to use compound cue retrieval, whereby stimuli serve as joint retrieval cues to select a response from long-term memory. In the present study, the authors tested how well a model of compound cue retrieval could account for a complex pattern of congruency effects arising from a procedure in which a cue, prime, and target were presented on each trial. A comparison of alternative models of prime-based effects revealed that the best model was one in which all stimuli participated directly in the process of retrieving a response, validating previous modeling efforts. Relations to current theorizing about response congruency effects and models of response selection in task switching are discussed.