  We compute one-loop corrections to the annihilation of non--relativistic
particles $\chi$ due to the exchange of a (gauge or Higgs) boson $\phi$ with
mass $\mu$ in the initial state. In the limit $m_\chi \gg \mu$ this leads to
the "Sommerfeld enhancement" of the annihilation cross section. However, here
we are interested in the case $\mu \lsim m_\chi$, where the one--loop
corrections are well--behaved, but can still be sizable. We find simple and
accurate expressions for annihilation from both $S-$ and $P-$wave initial
states; they differ from each other if $\mu \neq 0$. In order to apply our
results to the calculation of the relic density of Weakly Interacting Massive
Particles (WIMPs), we describe how to compute the thermal average of the
corrected cross sections. We apply this formalism to scalar and Dirac fermion
singlet WIMPs, and show that the corrections are always very small in the
former case, but can be very large in the latter. Moreover, in the context of
the Minimal Supersymmetric Standard Model, these corrections can decrease the
relic density of neutralinos by more than 1%, if the lightest neutralino is a
strongly mixed state.
