Over the past two decades, a new way of looking at handedness has emerged (see Prichard, E., Propper, R. E., & Christman, S. D. (2013). Degree of handedness, but not direction, is a systematic predictor of cognitive performance. Frontiers in Psychology, 4, 1–6), with an emphasis on degree (strong/consistent versus mixed/inconsistent) augmenting the traditional emphasis on direction (left versus right) of handedness. Much of this work has focused on main effects: e.g., inconsistent-handers show higher (or lower) performance than consistent-handers. However, many of these “main effects” are actually nested within higher order interactions: e.g., there are no handedness differences in a baseline/control condition, with handedness differences emerging in an experimental condition. Careful examination, though, of these interactions reveals an intriguing and predictable pattern: for integrated dual processes (e.g., episodic memory encoding versus retrieval), the interactions reflect larger effects in inconsistent-, relative to consistent-, handers. For independent, mutually exclusive dual processes (e.g., approach versus withdrawal), the interactions reflect larger effects in consistent-handers. It is argued that these patterns reflect the relative inability of (i) consistent-handers to integrate dual processes, and (ii) inconsistent-handers to keep independent dual processes separate. We also use this same theory to address higher order interactions involving changes in the experimental context as well as other individual difference factors, and make suggestions for future research.