We propose that the thinning of the plasma sheet during magnetospheric substorms is caused by an earthward gradient of the rate of magnetic merging (field annihilation) in the tail current sheet, which is in turn caused by the velocity-dependent access of plasma mantle particles to the current sheet. A simple model calculation based on this effect predicts a thinning time constant of the order of 1 hour, consistent with observations. The mechanism is also consistent with the observed correlation between plasma-sheet thinning and southward-directed magnetic field components in the solar wind.