A modified binary-collision-approximation algorithm allowing the proper order of the collisions in time was used to study cascades in Cu and Au at primary kinetic energies up to 100 keV. Nonlinearities were approximated by letting already-stopped cascade atoms become targets in later collisions, using an improved method of locating potential targets to extend the calculations to energies much higher than heretofore. Beside the effect of the approximate nonlinearity, the effect of thermal disorder in the targets was examined. Target redisplacements reduce the damage in Cu by 3% at most, but in Au they reduce it by amounts up to 20% at 100 keV. Thermal disorder is also important: by disrupting crystal effects, the damage is reduced significantly.