OK, well I don't know the Parsec types and function names off the top of my head, but suppose I have the following: runParser :: Parser a b -> [a] -> Either ParseError b parseHuffmanTable :: [x] -> Parser Word8 (HuffmanTable x) parseHuffmanPayload :: HuffmanTable x -> Parser Word8 [x] parseRLE :: Parser Word8 [Word8] Now, if I want to just do without the RLE bit, I can do parseHuffman :: [x] -> Parser Word8 x parseHuffman xs = do table <- parseHuffmanTable xs parseHuffmanPayload table But if I want to add an RLE layer to just the Huffman table... erm... OK, I'm stuck now. :-S 1. How do I run the input through parseRLE and *then* through parseHuffmanTable? 2. How do I get parseHuffmanPayload to continue from where parseRLE left off? (How do I get parseRLE to not parse the entire input, for that matter...)