We report on an extensive computational investigation of the effect of the surface barrier on hysteresis losses. These model calculations reveal that the losses can be substantially diminished by lowering the height of the surface barrier. The calculations were carried out for planar (ribbon) and for cylindrical (wire) geometry with the applied magnetic field directed along the surface(s) of the sample and swept between (i) 0 and Hmax. (half-wave cycle) and (ii) ±Hmax(full-wave cycle). We examined the behavior for amplitudes below and above that required for full penetration of the flux disturbance to the center of the specimen. We have explored the phenomena for two extremal types of bulk pinning, namely the Bean-London (Jc= α1) and the Kim-Anderson (Jc= α0/B) approximations. We have, for simplicity, assumed that the barrier height is field independent and either symmetric (opposing flux entry and exit equally) or asymmetric (opposing flux entry only).