  We demonstrate that CPMG and XYXY decoupling sequences with non-ideal $\pi$
pulses can reduce dipolar interactions between spins of the same species in
solids. Our simulations of pulsed electron spin resonance (ESR) experiments
show that $\pi$ rotations with small ($<$~10\%) imperfections refocus
instantaneous diffusion. Here, the intractable N-body problem of interacting
dipoles is approximated by the average evolution of a single spin in a changing
mean field. These calculations agree well with experiments and do not require
powerful hardware. Our results add to past attempts to explain similar
phenomena in solid state nuclear magnetic resonance (NMR). Although the
fundamental physics of NMR are similar to ESR, the larger linewidths in ESR and
stronger dipolar interactions between electron spins compared to nuclear spins
preclude drawing conclusions from NMR studies alone. For bulk spins, we also
find that using XYXY results in less inflation of the deduced echo decay times
as compared to decays obtained with CPMG.
