  We study the $2\rightarrow1$ process of electron-positron pair annihilation
to a single photon in a plane-wave background. The probability of the process
in a pulsed plane wave is presented, and a locally constant field approximation
is derived and benchmarked against exact results. The stricter kinematics of
annihilation (compared to the $1\rightarrow2$ processes usually studied) leads
to a stronger dependence on the incoming particle states. We demonstrate this
by studying the effect that initial state wavepackets have on the annihilation
probability. The effect of annihilation in a distribution of particles is
studied by incorporating the process into Monte Carlo simulations.
