NMR spin echo measurements of C-13 in C60, Y-89 in Y2O3, and Si-29 in silicon are shown to defy conventional expectations when more that one pi pulse is used. Multiple pi-pulse echo trains may either freeze our or accelerate the decay of the signal, depending on the pi-pulse phase. Average Hamiltonian theory, combined with exact quantum calculations, reveals an intrinsic cause for these coherent phenomena: the dipolar coupling has a many-body effect during any real, finite pulse.