Observations from the SWICS instrument on Ulysses reveal that there is little evidence for the acceleration of interstellar pick‐up ions at the forward and reverse shocks which surround Co‐rotating Interactions Regions (CIR's) in the solar wind. Rather, the pick‐up ions exhibit strong acceleration in regions within the CIR where there are increased variations in the magnitude of the magnetic field. A simple model is presented in which the pick‐up ions are statistically accelerated by transit‐time damping the magnitude variations. The model yields the observed distribution functions for the accelerated pick‐up ions.