<p>Reading a book in a coffee shop requires focusing on the task at hand and ignoring task-irrelevant distraction (cognitive stability), while setting aside the book to answer a phone call requires the ability to switch between tasks (cognitive flexibility). Stability and flexibility are often conceptualized as opposing ends of a one-dimensional stability–flexibility continuum, whereby increasing stability (prioritizing task focus) reciprocally reduces flexibility (a readiness to switch tasks), and vice versa. Recent evidence, however, has supported a two-dimensional stability–flexibility relationship, whereby stability and flexibility can be maintained at high levels simultaneously when necessary. Here, we adjudicate between the one- and two-dimensional accounts by fitting competing models to two cued task switching datasets that manipulated the proportion of switch trials (driving contextual adjustments in flexibility) and cross-task congruency effects (driving contextual adjustments in stability). We consider two one-dimensional models: one that assumes a rigid tradeoff where any increase in stability results in a decrease in flexibility, and a more flexible, generalized model that allows but does not enforce such a direct tradeoff. We compare these to two two-dimensional models, one which enforces a strict independence of stability and flexibility, and an unrestricted model that allows interactions between them. Both two-dimensional models, but neither one-dimensional model, were capable of reproducing key behavioral patterns in the original data set. However, the unrestricted two-dimensional model had the best predictive power, indicating that stability and flexibility, while distinct, may trade off in individual- and context-specific ways.</p>