When you encrypt something, the output is highly entropic and there will be no redundancy in the text. Compression works by removing redundancy from the file, so, given that there is no redundancy in an encrypted file there will be no compression.

See... this, for example. Pay particular reference to the section which states "Compression after encryption is silly. If an encryption algorithm is good, it will produce output which is statistically indistinguishable from random numbers and no compression algorithm will considerably compress random numbers. On the other hand, if a compression algorithm succeeds in finding a pattern to compress out of an encryption's output, then a flaw in that algorithm has been found. In the majority of encryption utilities (e.g., PGP ) the data is first compressed before it is actually encrypted."