A digital media encoder/decoder uses a flexible quantization technique that provides the ability to vary quantization along various dimensions of the encoded digital media data, including spatial, frequency sub bands and color channels. The codec utilizes a signaling scheme to signal various permutations of flexible quantization combinations efficiently for primary usage scenarios. When a choice of quantizer is available, the codec efficiently encodes the current quantizer by defining a subset of quantizers and indexes the current quantizer from the set.