The sawtooth control mechanism in plasmas employing toroidally propagating ion cyclotron resonance waves is extended. The asymmetrically distributed energetic passing ions are shown to modify the ideal internal kink mode when the position of the minority ion cyclotron resonance resides within a narrow region close to the q=1 surface. An analytical treatment of the internal kink mode in the presence of model distribution function with parallel velocity asymmetry is developed. The fast ion mechanism explains the strong sensitivity of sawteeth to resonance position, and moreover is consistent with dedicated Joint European Torus [F. Romanelli, Nucl. Fusion 49, 104006 (2009)] experiments which controlled sawteeth despite negligible current drive.