Techniques and tools for prediction of spectral coefficients in encoding and decoding are described herein. For certain types and patterns of content, coefficient prediction exploits correlation between adjacent spectral coefficients, making subsequent entropy encoding more efficient. For example, an audio encoder predictively codes quantized spectral coefficients in the quantized domain and entropy encodes results of the predictive coding. Or, for a particular quantized spectral coefficient, an audio decoder entropy decodes a difference value, computes a predictor in the quantized domain, and combines the predictor and the difference value.