A joint aim of cognitive psychology and neuropsychology has been the decomposition of mental function-the isolation and characterization of basic processes underlying behavior. By convention, the principal techniques used to identify such processes are based on functional dissociation-the observation of selective effects of variables on tasks. Yet, despite their widespread use, the inferential logic associated with these techniques is flawed in two ways. First, it is possible to posit single processes that mimic both single and double dissociation; and second, observation and interpretation of both kinds of dissociation are limited by an assumption of selective influence that most, if not all, psychologists would now reject as false. The aims of this article are twofold: (a) to review and make explicit the inferential limits of single and double dissociation; and (b) to introduce a new technique that overcomes these limits. Called reversed association, this new technique is defined as any nonmonotonic relation between two tasks of interest. We argue that reversed association, in place of functional dissociation, offers a sounder basis for inferring the number of functionally independent processes underlying performance and, having fewer assumptions, offers researchers greater scope for discovering such processes and determining their nature and effects.