Dual-process theory hypothesizes that recognition memory depends on 2 distinguishable memory signals. Recollection reflects conscious recovery of detailed information about the learning episode. Familiarity reflects a memory signal that is not accompanied by a vivid conscious experience but nonetheless enables participants to distinguish recently experienced probe items from novel ones. This dual-process explanation of recognition memory has gained wide acceptance among cognitive neuroscientists and some cognitive psychologists. Nonetheless, its difficulty in providing a quantitatively satisfactory description of performance has precluded a consensus not only regarding the theoretical structure of recognition memory but also about how to best measure recognition accuracy. In 2 experiments we show that neither the standard formulation of dual-process signal detection (DPSD) theory nor a widely used single-process model called the unequal-variance signal-detection (UVSD) model provides a satisfactory explanation of recognition memory across different types of stimuli (words and travel scenes). In the variable-recollection dual-process (VRDP) model, recollection fails for some old probe items, as in standard formulations of DPSD, but gives rise to a continuous distribution of memory strengths when it succeeds. The VRDP can approximate both the DPSD and UVSD. In both experiments it provides a consistently superior fit across materials to the superset of the DPSD and UVSD. The VRDP offers a simple explanation of the form of conjoint item-source judgments, something neither the DPSD nor UVSD accomplishes. The success of the VRDP supports the core assumptions of dual-process theory by providing an excellent quantitative description of recognition performance across materials and response criteria. (Contains 10 figures, 5 tables, and 8 footnotes.)