Parallel table lookups are implemented using variable Mux instructions to reorder data. Table data can be represented in a "table" register, while the desired ordering can be represented in an "Index" register. A direct variable Mux instruction can specify the table register and the index register as arguments, along with a result register. The instruction writes at least some of the data from the table register into the result register as specified in the index register. If the entire table cannot fit within a single register, entries can be divided between two or more table registers. An indirect variable Mux instruction can specify both a table-register-select register and a subword-location-select register. Both the direct and indirect Mux instructions can be used with entry data that is divided in accordance with significance between registers. In that case, plural Mux instructions are used with UnPack instructions that concatenate portions of the table entries.