Don't compress then encrypt. It doesn't matter in this use case, but it matters very much in others. When attackers have chosen plaintext (which is virtually always), they can exploit compression to create a traffic-analytic side channel. This is the CRIME and BREACH attack on TLS, for instance.

Schneier, in Applied Cryptography (which: avoid) recommended compressing before encrypting. That was bad advice. Compression and encryption interact in treacherous ways. Get of out the habit of combining them.