Numerical dispersion in finite-difference (FD) modeling produces coherent artifacts, severely constraining the resolution of advanced imaging and inversion techniques. Conventionally, numerical dispersion is reduced by increasing the order of accuracy of the FD operators, and we resign ourselves to paying the high computational cost that is incurred. Assuming no spatial dispersion, we have found that FD time dispersion is independent of the medium velocity and the spatial grid for propagation, and only depends on the time-stepping scheme and the propagation time. Based on this observation, we have devised postpropagation filters to collapse the time-dispersion effect of FD modeling. Our dispersion correction filters are designed by comparing the input waveform with dispersive waveforms obtained by 1D forward modeling. These filters are then applied on multidimensional shot records to eliminate the time dispersion by two schemes: (1) stationary filtering plus interpolation and (2) nonstationary filtering. We have found with 1D and 2D examples that the time dispersion is effectively removed by our postpropagation filtering at a negligible cost compared with a higher order modeling scheme.