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This paper discusses ways to avoid and/or mitigate biases in polarimetric variables inherent to agile-beam planar phased-array radars. Two bias-avoiding schemes produce unbiased estimates of the polarimetric backscattering covariance matrix which are then combined into bias-free polarimetric variables. One concerns full polarimetric measurements and calls for adjusting the amplitudes and phases of the array elements so that the transmitted field equals that generated by a mechanically steered polarimetric weather radar antenna; this is followed by an additional adjustment of the received fields. The second scheme is also applicable to full polarimetric measurements but involves adjustments only of the received fields. Crucial to both schemes is decoupling of the Doppler effects from the terms of the covariance matrix. It is a significant part of the bias issue that had not been previously addressed. A scheme to reduce bias applicable to nondepolarizing media (i.e., diagonal backscattering matrix) is also addressed; it calls for multiplication of the fields received by each dipole as opposed to a combination of multiplication and addition required for full correction. The schemes are applied to the alternate transmission and simultaneous reception polarimetric mode and the simultaneous transmission and simultaneous reception mode.