The process-dissociation model has stimulated important advances in the study of dual-process conceptions of memory. The authors review some limiting properties of that model and consider the degree of support for its parent theory (the recollection-familiarity distinction). A 2nd-generation model (conjoint recognition) is proposed that addresses these limitations and supplies additional capabilities, such as goodness-of-fit tests, the ability to measure dual processes for false-memory responses, and statistical procedures for testing within- and between-conditions hypotheses about its parameters. The conjoint-recognition model also implements an alternative theoretical interpretation (the identity-similarity distinction of fuzzy-trace theory). Worked applications to data are provided.