In an important class of flux pumps, the load current is switched back and forth between two parallel paths each cycle. It is shown that if this is done by driving a current-carrying path resistive, heat will be dissipated equal to the change in persistent current inductive energy before and after the switching process. This heat is independent of path resistance. The efficiency of pumps operated in this mode goes to zero as the pumped current approaches its maximum value. It is shown, however, that this energy dissipation can be eliminated by using electromagnetic induction to cancel the current in a branch that is to be driven resistive. In this mode of operation, the switching dissipation at low temperature can be made arbitrarily small. Comparison with published data confirms the analysis.