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We present a simple approach to constructing phase-only tapers for regular planar arrays that is analogous to the instantaneous-frequency approach classically used to construct FM-chirp waveforms with high time-bandwidth products. Design experiments for a large triangular-grid array show that the crude results yielded by this method when aperture-beamwidth products are modest can sometimes be “tweaked” into reasonableness. We conjecture that such a taper would improve upon the usual uniform-weight starting point for a nonlinear-optimization approach that seeks out a local optimum. Specific design examples presented here nominally aim to approximate a brick-wall beam and a variant of a Gaussian beam.