The sharpness-aware minimization (SAM) procedure recently gained increasing attention due to its favorable generalization ability to unseen data. SAM aims to find flatter (local) minima, utilizing a minimax objective.  An immediate challenge in the application of SAM is the adjustment of two pivotal step sizes, which significantly influence its effectiveness. We introduce a novel, straightforward approach for adjusting step sizes that adapts to the smoothness of the objective function, thereby reducing the necessity for manual tuning. This method, termed Smoothness-Adaptive SAM (SA-SAM), not only simplifies the optimization process but also promotes the method's inherent tendency to converge towards flatter minima, enhancing performance in specific models.