  The locally constant field approximation (LCFA) has to date underpinned the
numerical simulation of quantum processes in laser-plasma physics and
astrophysics, but its validity has recently been questioned in the parameter
regime of current laser experiments. While improvements are needed, literature
corrections to the LCFA show inherent problems. Using nonlinear Compton
scattering in laser fields to illustrate, we show here how to overcome the
problems in LCFA corrections. We derive an "LCFA+" which, comparing with the
full QED result, shows an improvement over the LCFA across the whole photon
emission spectrum. We also demonstrate an implementation of our results in the
type of numerical code used to design and analyse intense laser experiments.
