For people who haven't dealt with this - a good encryption scheme produces output which you can't tell apart from a purely random stream of bits - it has very high entropy, and is therefore not compressible.

Thanks for clarifying this. That must mean then: first encrypt, then compress?

Compress than encrypt.

And this has some pitfalls as well, ciphertext in general has about the same length as the plaintext, so compression rate can be used to infer some information about the plaintext. It's more of a problem with interactive protocols than with backups, but still worth keeping in mind.