Hypotheses about decision processes are often formulated qualitatively and remain silent about the interplay of decision, memorial, and other cognitive processes. At the same time, existing decision models are specified at varying levels of detail, making it difficult to compare them. We provide a methodological primer on how detailed cognitive architectures such as ACT-R allow remedying these problems. To make our point, we address a controversy, namely, whether noncompensatory or compensatory processes better describe how people make decisions from the accessibility of memories. We specify 39 models of accessibility-based decision processes in ACT-R, including the noncompensatory recognition heuristic and various other popular noncompensatory and compensatory decision models. Additionally, to illustrate how such models can be tested, we conduct a model comparison, fitting the models to one experiment and letting them generalize to another. Behavioral data are best accounted for by race models. These race models embody the noncompensatory recognition heuristic and compensatory models as a race between competing processes, dissolving the dichotomy between existing decision models.