In most integration schemes for the Maxwell's equations, damping and distortion errors are strongly dependent on the size of the time step in relation to the size of the spatial discretization Δx. The disadvantage of strong dependence on this ratio becomes evident when one computes the solution on nonuniform meshes. A systematic way for arriving at a scheme that can operate accurately on nonuniform meshes is presented here. Performance of a higher-order scheme is compared with that of another recently developed scheme on a ramp grid. ¿ American Geophysical Union 1996