Spectral spreading in radar systems is a concern that is related to the radar waveform. This paper describes a procedure to optimize a linear frequency-modulated chirp waveform for a desired ambiguity function while meeting spectral requirements. The minimax approach used for the optimization is described, and some example results for the optimization are presented. The integration of bench-top spectrum analyzer measurements into the optimization is presented, and the way forward in terms of measurement-based optimization is discussed.