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, compared 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 analyze intense laser experiments.