The paper discusses the effects of Fresnel ripples on the suppression of peak time sidelobes in low time-bandwidth (TB) product linear-FM pulse compression systems employing internally Hamming weighted compression filters. Two methods for the reduction of these effects are investigated. The first, amplitude tapering of the rectangular FM pulse, yields significantly diminished sidelobes forTBproducts less than about 100 and is of particular interest for spectrum analysis. The second, applicable to short risetime high-power radar transmitters, is cubic phase predistortion of the rectangular transmitted pulse. This procedure is found to be very effective forTBproducts less than about 50 (e.g. about 10 dB improvement forTB=10 compared with usual chirp). Both techniques force the fall-off of far sidelobes. Computed results on the achievable sidelobe suppression are presented as a function of theTBproduct and compared with conventional Hamming weighting. Finally, it is shown that the superior Doppler performance of linear FM is not affected by the discussed waveform modifications.