We propose and implement a technique to enable random access in any data compressor. With the transformed compressor, arbitrary requests to a compressed file's content can be served without decompressing large amounts of unrequested data. A comprehensive performance study is carried out: A cloud storage pod is used to examine the compression and random access capabilities achieved with eight popular data compression tools for three diverse data types under different cache conditions. We compare the speed of random accesses to the uncompressed file and the compressed, to quantify the impact of having to decompress during retrievals. Our experiments reveal that the transformed compressor allows files to be stored in a compressed format, while also allowing arbitrary requests to the file's content to be served efficiently.