  Pumping of charge in phase-coherent mesoscopic systems due to the
out-of-phase modulation of two parameters has recently found considerable
interest. We investigate the effect of inelastic processes on the adiabatically
pumped current through a two terminal mesoscopic sample. We find that the loss
of coherence does not suppress the pumped charge but rather an additional
physical mechanism for an incoherent pump effect comes into play. In a fully
phase incoherent system the pump effect is similar to a rectification effect.
