We experimentally demonstrate how divided-pulse nonlinear compression can be used to improve the temporal contrast of a laser pulse train while simultaneously temporally compressing the pulses. We measure a contrast improvement of almost four orders of magnitude on a nanosecond time scale and temporally compress the pulses from 1.2 ps to 187 fs. The efficiency of our method is also competitive with other contrast improvement methods, with 72% efficiency measured for the main pulse. We expect the method will be useful in the continuing development of high-power, Yb regenerative amplifiers, which suffer from both significant prepulses and relatively long pulse durations.