We present a theory for the longitudinal averaged satellite sweeping rate in an offset, tilted dipole magnetic field. We include the reductions in the sweeping rate when the moon radius is not large compared to the gyroradius or the azimuthal drift distance during a bounce period. With a large tilt angle between the magnetic and rotation axes, moons make large excursions in dipole L value, and more than one moon can sweep at a given L. The sweeping rate peaks at the minimum L for each moon. If the gyroradius is large, additional peaks can occur when the particle mirrors near the moon latitude. To illustrate the theory, sweeping rates are evaluated for parameters relevant to the observations at Uranus by the Voyager 2 Low Energy Charged Particles Experiment. Calculated sweeping rates for ions and electrons are typically two or three orders of magnitude less than the strong-diffusion loss rate. The observation of sweeping signatures at Uranus would imply that pitch-angle scattering there occurs at a rate far below the strong-diffusion limit, contrasting with the situation for energetic ions in the inner Jovian magnetosphere. ¿ American Geophysical Union 1987