Whether recognition memory is mediated by discrete or continuous processes has long been the subject of debate. Deemed "the ignored alternative" by Kellen, Erdfelder, Malmberg, Dubé, and Criss (2016), Luce's (1963) low-threshold model is a discrete model that describes data thought to be indicative of continuous mediation. Kellen et al. found that the low-threshold model describes data quantitatively as well as signal detection theory, a continuous model. We replicate that finding here across 8 experiments. More interestingly, we find that this equivalence is because of the 2 models fitting different aspects of the data--the low-threshold model better fits strongly encoded stimuli, and signal detection theory better fits weakly encoded stimuli. An alternative framework for recognition memory may be necessary--one that incorporates a control process that can induce either continuous or discrete mediation. According to this framework, meta-cognitive judgments regarding the strength of an item may induce the strategic discretization of memory.