Efficient operations in image or video decoding. For example, a tool such as an image or video decoder receives and decodes encoded data for a picture in a bitstream. As part of the decoding, the tool adapts a multi-symbol lookup table to use in decoding of symbols then decodes the symbols using the multi-symbol lookup table, producing exactly correct results. The tool can also perform selectively truncated inverse frequency transforms. For a given block, the tool identifies upper horizontal and vertical frequencies among non-zero coefficients for the block and, based on the upper frequency values, selectively applies a simplified inverse frequency transform to transform coefficients for the block without hurting decoding quality. Using restart markers in the bitstream, the tool can organize multiple blocks of the picture as partitions. The tool decodes at least some of the partitions in parallel on a partition-by-partition basis using multiple processing cores.