It has long been known that cues can be used to improve performance on memory recall tasks. There is evidence to suggest additional cues provide further benefit, presumably by narrowing the search space. Problems that require integration of two or more cues, alternately referred to as memory intersections or multiply constrained memory problems, could be approached using several strategies, namely serial or parallel consideration of cues. The type of strategy implicated is essential information for the development of theories of memory, yet evidence to date has been inconclusive. Using a novel application of the powerful Systems Factorial Technology (Townsend & Nozawa, 1995) we find strong evidence that participants use two cues in parallel in free recall tasks - a finding that contradicts two recent publications in this area. We then provide evidence from a related recognition task showing that while most participants also use a parallel strategy in that paradigm, a reliable subset of participants used a serial strategy. Our findings suggest a theoretically meaningful distinction between participants strategies in recall and recognition based intersection memory tasks, and also highlight the importance of tightly controlled methodological and analytic frameworks to overcome issues of serial/parallel model mimicry.