The current study aimed to uncover the structure of common latent processes underlying the execution of several tasks that hypothetically measure spontaneous and adaptive cognitive flexibility, providing evidence for their convergent validity. A group of healthy volunteers (N = 121) completed two sets of tasks to assess spontaneous and adaptive cognitive flexibility. Spontaneous flexibility measures included a divergent thinking test (to assess fluency and flexibility of thinking) and a verbal fluency test. Adaptive flexibility measures involved a set-switching test as a measure of switch costs and an attentional set-shifting test as a measure of learned irrelevance and perseveration). A vocabulary knowledge test provided a proxy measure of crystallized intelligence. Hierarchical cluster analysis using Ward's method revealed the existence of two separate subgroups of variables. The first group comprised fluency and flexibility of thinking, crystallized intelligence, verbal fluency, and switch costs. The second group included attentional shift variables, that is, learned irrelevance and perseveration. We consider these results meaningful and indicative of two separate factors contributing to cognitive flexibility: (a) speed of switching and (b) overcoming of prepotent responses. We discuss the implications of our results for the assessment of cognitive flexibility.