  Electromagnetic ion cyclotron waves are expected to pitch-angle scatter and
cause atmospheric precipitation of relativistic ($> 1$ MeV) electrons under
typical conditions in Earth's radiation belts. However, it has been a
longstanding mystery how relativistic electrons in the hundreds of keV range
(but $<1$ MeV), which are not resonant with these waves, precipitate
simultaneously with those $>1$ MeV. We demonstrate that, when the wave packets
are short, nonresonant interactions enable such scattering of $100$s of keV
electrons by introducing a spread in wavenumber space. We generalize the
quasi-linear diffusion model to include nonresonant effects. The resultant
model exhibits an exponential decay of the scattering rates extending below the
minimum resonant energy depending on the shortness of the wave packets. This
generalized model naturally explains observed nonresonant electron
precipitation in the hundreds of keV concurrent with $>1$ MeV precipitation.
