[hackinthebochs]

Definitely compress first. While it is true that there is the same amount of entropy before and after encryption, you'll never be able to identify it from the bitstream (otherwise your encryption is broken). Compression works by understanding statistical patterns in the process that is creating the data stream, and encoding the data based on this information to achieve a reduced stream size. An encrypted stream is generally assumed to be indistinguishable from random data, so you won't get nearly as much (if any) compression from this pseudorandom stream.