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The authors present a computationally efficient method for designing practical radar transmit waveforms that maximize the signal-to-interference-plus-noise ratio (SINR) in a known additive coloured Gaussian noise environment. The problem reduces to a non-linear constrained optimisation in which the authors seek the SINR-maximising transmit waveform that has a specified envelope and an acceptable autocorrelation sequence (ACS). The waveform ACS can be constrained either directly or indirectly. The direct approach involves forcing the ACS magnitude below a specified level at each lag. This provides the greatest control over the waveform ACS, but it is too computationally demanding for many realistic problem sizes. Indirect methods of ACS constraint can be computationally less demanding, but they afford only inexact control over the waveform ACS. The leading indirect approach, which relies on the so-called similarity constraint, requires significantly fewer calculations than the direct approach, but it provides significantly less SINR improvement. The indirect approach presented here relies on a parametrisation of the phase perturbations of a linear frequency modulated waveform. This approach requires fewer calculations than the direct approach, and can provide more SINR improvement than the similarity constraint approach. As such, this new approach may be preferable when computation time is limited.