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Resonances and/or singularities during measurement and calibration often limit the precision of acoustic impedance spectra. This paper reviews and compares several established techniques, and describes a technique that incorporates three features that considerably improve precision. The first feature is to minimize problems due to resonances by calibrating the instrument using up to three different acoustic reference impedances that do not themselves exhibit resonances. The second involves using multiple pressure transducers to reduce the effects of measurement singularities. The third involves iteratively tailoring the spectrum of the stimulus signal to control the distribution of errors across the particular measured impedance spectrum. Examples are given of the performance of the technique on simple cylindrical waveguides.