Studies focusing on unsupervised categorization and sorting behavior have traditionally identified and empirically isolated a few select strategies frequently employed by observers, one-dimensional (SD), family resemblance (FR), and exclusive-or (XOR). To date, these investigations have mostly involved creating sets of multidimensional stimuli that directly contrast utilization of these strategies coupled with task or stimulus property manipulations to see their effects on categorization and sorting behavior. Currently, we extend on this methodological approach by having observers sort integral-dimension stimuli for two recently developed constrained unsupervised categorization tasks employing three-dimensional Boolean category structures. These structures instantiate six different sorting strategies, including the aforementioned SD, FR, and XOR strategies. Additionally, we connect the prevalence of the strategies observed across both tasks to previous investigations employing separable stimuli with the same tasks and underlying Boolean category structures. In comparison, our results indicate significant reductions in rule-like sorting behavior (SD or XOR) across multiple structures with the integral stimuli. Associated with this decrease in SD and XOR behavior was a corresponding increase in FR and FR-related sorting behavior. Finally, we assess how well generalized representational information theory and the simplicity model can account for the pattern of results across both experimental paradigms and stimulus sets. In general, a formal model derived from "GRIT" outperforms the simplicity model, accounting for nearly the entire range of unsupervised sorting behavior (SD, FR, XOR) observed across the separable and integral tasks.