  We derive an approximation to QED effects in strong background fields which
can be employed to improve numerical simulations of laser-particle collisions.
Treating the laser as a plane wave of arbitrary intensity, we split the wave
into fast (carrier) and slow (envelope) modes. We solve the interaction
dynamics exactly for the former while performing a local expansion in the
latter. This yields a `locally monochromatic' approximation (LMA), which we
compare with exact spectra for nonlinear Compton scattering and nonlinear
Breit-Wheeler pair production, for realistic laser pulse durations. We show
that, as an improvement over the commonly used `locally-constant field'
approximation, the LMA exactly reproduces the correct low energy behaviour of
particle spectra, as well as the position and amplitude of harmonic features.
