We have studied the charge-density-wave (CDW) current conversion process in NbSe3 wire structures of mesoscopic dimensions. A significant reduction of the phase-slip voltage associated with this conversion is observed if the spacing between current contacts is smaller than a few &mgr;m. This reduction cannot be explained with existing models of CDW current conversion. We suggest that single phase-slip events play a central role in micron-sized systems. The removal and addition of wave fronts may then become correlated in time.