1. A method of decoding digital media, comprising: with a computer, receiving compressed digital image data, the compressed digital image data having been partitioned along more than one dimension; determining multiple sets of quantization parameter indices from signals in the compressed digital image data, the compressed digital image data having been quantized across more than one partitioned dimension of the digital image data, the signals indicating whether quantization parameter indices used during decoding vary within a frequency band dimension and within a color channel dimension, the quantization parameter indices available across the frequency band dimension including, for a given set of the multiple sets of quantization parameter indices, a first quantization parameter index for one or more DC components, a second quantization parameter index for multiple low-pass components, and a third quantization parameter index for multiple high-pass components; for each of multiple macroblocks of the compressed digital image data: selecting one of the multiple sets of quantization parameter indices based on a value signaled for the macroblock; and determining one or more quantization parameters for the selected set of quantization parameter indices; dequantizing the compressed digital image data in accordance with the determined quantization parameters; applying an inverse of a block transform to blocks of the dequantized digital image data; and outputting decompressed digital image data, wherein: (a) the multiple high-pass coefficients are AC coefficients from first transforms of values of blocks of a macroblock; (b) the multiple low-pass coefficients are AC coefficients from a second transform of DC coefficients from the first transforms; and (c) the one or more DC coefficients include a DC coefficient from the second transform of the DC coefficients from the first transforms.