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To cope with the effects of channel errors, robust adaptive quantization schemes contain a leakage parameter in the step-size adaptation algorithm. Unfortunately, this mechanism also introduces its own distortion in the form of reduced dynamic range of the step size which causes the signal-to-noise ratio to drop appreciably at the far ends of the range of input signal intensities typically associated with speech applications. A method for compensating for the leakage-induced distortion is proposed here. It consists of a generalization of the adaptive quantizer with the novelty contained entirely in the decoding procedure. Whereas the reconstruction or decoded values in existing adaptive quantizers are proportional to the adapted step size, with the prespecified and fixed reconstruction parameters giving the constants of proportionality, the generalization will have these parameters replaced by reconstruction functions of the time-evolving step size. The sole time-varying parameter in the generalized quantizer is, as originally, the step size which is adapted in exactly the same manner as in existing robust quantizers. Two straightforward methods for the synthesis of the reconstruction functions are presented. The first is analytic while the second is a method for generating the functions through simulations. Computed results for two examples are presented. In the first example, the input signals are independent, Gaussian random variables. In the second example, the inputs are correlated and generated by a first-order Markov model. The communication system is adaptive differential PCM. In both examples, the generalized systems perform consistently better than existing systems and give significant improvements in SNR for signal intensities at the extremities of a 50 dB range.