Innovations in the use of base color index map (“BCIM”) mode during encoding and/or decoding simplify implementation by reducing the number of modifications made to support BCIM mode and/or improve coding efficiency of BCIM mode. For example, some of the innovations involve reuse of a syntax structure that is adapted for transform coefficients to instead signal data for elements of an index map in BCIM mode. Other innovations relate to mapping of index values in BCIM mode or prediction of elements of an index map in BCIM mode. Still other innovations relate to handling of exception values in BCIM mode.