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The successful application of pulse compression techniques depends largely on reduction of the range sidelobes associated with the compressed pulse waveform. It is shown that the calculation of sidelobe levels in previously published data is not exact when low sidelobes are called for, since the effects of spectrum amplitude ripple in contributing to the range sidelobes have either been ignored or not stated. This paper presents more recent information on this subject, introducing a model of the Fresnel spectrum that permits a more accurate calculation of the compressed pulse sidelobe structure. Additional spectrum-associated paired-echo range sidelobes are predicted as a result of the model, and are observed in practice, having peak values up to 15 db larger than those derived on the basis of the idealized spectrum assumed in earlier studies. It is shown experimentally that elimination of the spectrum amplitude ripple results in removal of these paired-echo sidelobes, thus allowing more efficient use of the signal energy when low side-lobe levels are required. A predistorted linear FM pulse compression signal is presented as a realizable means for exerting control over the spectrum function. This new pulse compression technique does not require pulse envelope or rise-time shaping at the transmitter, and thus has application to high-power systems. Experimental waveforms illustrate the reduction of the spectrum-associated paired-echo sidelobes with the modified linear FM signal, and also show that the remaining range sidelobes do not appreciably increase as a function of Doppler shift.