An increase of the C-13 NMR linewidth with increasing rate of magic-angle spinning observed for certain solids under high-power proton decoupling is shown to be a consequence of the slowing of proton spin exchange at high spinning speeds. This accentuates the effects of off-resonance decoupling and leads to an inhomogeneous broadening of the C-13 lines. It is demonstrated that periodic phase-modulated irradiation is able to restore the condition of on-resonance decoupling and to maintain the spectral resolution observed at moderate spinning speeds, where spin exchange is more efficient. (C) 1994 Academic Press, Inc.