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. ¿ American Geophysical Union 1996