Described herein are methods and devices that employ parallel compression of image data using a lossless compressor and a quantization compressor. As described, the lossless compressor generates a variable length compressed bit stream and the quantization compressor generates a fixed length compressed bit stream. The fixed length bit stream is always equal in size to a size requirement of an output memory block. The variable length bit stream may be stored in the output memory block unless it exceeds the memory requirement in size, in which case the fixed length bit stream may be stored to the output memory block.