The notion of a multiple description quantizer (MDQ) includes providing multiple distortion levels. If a human observer is involved, the design of MDQ requires a suitable distortion measure to achieve a graceful quality degradation in the case of description losses. While the mean squared error is a ubiquitous distortion measure for many classic MDQ schemes, it is known to be perceptually relevant only at low distortions. We propose a new MDQ designed according to an unconventional distortion criterion that combines the mean squared error with a constraint on the probability distribution of the reconstructed signal. The performance of the new MDQ is shown to approach that of the classic MDQ asymptotically as rate increases. However, once applied in the context of transform audio coding, the new MDQ significantly outperforms a classic MDQ in perceptual tests. The new scheme is suitable for a wide range of distortions and renders a seamless transition between coding that preserves signal features and coding of a waveform.