Methods of palette coding to reduce the required coding process are disclosed. According to one method, smaller blocks are derived from a large block. The histogram of the large block is derived based on the histograms of smaller blocks in the large block. According to another method, one or more palette tables are derived based on multiple blocks. One palette table is used for each of the multiple blocks. According to yet another method, index map transpose is performed in the parsing stage according to the transpose flag of the index map. Accordingly, a buffer to store the transpose flags can be saved. According to still yet another method, the palette predictor update is performed using an index mapping table to avoid the need for shuffling the contents of the palette predictor stored in a palette buffer.