Innovations in control and use of chroma quantization parameter (“QP”) values that depend on luma QP values. More generally, the innovations relate to control and use of QP values for a secondary color component that depend on QP values for a primary color component. For example, during encoding, an encoder determines a QP index from a primary component QP and secondary component QP offset. The encoder maps the QP index to a secondary component QP, which has an extended range. The encoder outputs at least part of a bitstream including the encoded content. A corresponding decoder receives at least part of a bitstream including encoded content. During decoding, the decoder determines a QP index from a primary component QP and secondary component QP offset, then maps the QP index to a secondary component QP, which has an extended range.