Flux-correction allows to reduce or even remove overshoot occuring when Lax-Wendroff methods are used to calculate onedimensional flow. There is a whole family of methods [3] depending on two parameters, whose optimal values are derived. One controls the amount of diffusion to reduce overshoot, the other determines removal of this diffusion as far as overshoot does not reappear, thus largely retaining accuracy of the employed Lax-Wendroff method.