Airport Surveillance Radar (ASR) manufacturers are proposing the use of non-linear FM pulse compression in their all solid state radars. However there is concern that the use of pulse compression will limit the radar's performance. High range sidelobes can cause poor performance in both target and weather detection. The theory of nonlinear FM pulse compression is derived along with a method of minimizing the sidelobes using a minimum mean square error (MMSE) technique. The results of a computer program using the MMSE technique show that very low sidelobe levels of more than 100 dB down may be achieved. These very low sidelobes are affected by filter misalignment, target Doppler, and by transmitter phase errors or stability. Curves are presented demonstrating these effects. We also show how filter misalignment can be corrected by receiver filtering. The methods presented here are general enough to be used to assess the performance of proposed non-linear FM waveform radars.