An audio encoder and decoder use architectures and techniques that improve the efficiency of quantization (e.g., weighting) and inverse quantization (e.g., inverse weighting) in audio coding and decoding. The described strategies include various techniques and tools, which can be used in combination or independently. For example, an audio encoder quantizes audio data in multiple channels, applying multiple channel-specific quantizer step modifiers, which give the encoder more control over balancing reconstruction quality between channels. The encoder also applies multiple quantization matrices and varies the resolution of the quantization matrices, which allows the encoder to use more resolution if overall quality is good and use less resolution if overall quality is poor. Finally, the encoder compresses one or more quantization matrices using temporal prediction to reduce the bitrate associated with the quantization matrices. An audio decoder performs corresponding inverse processing and decoding.