Encryption, Compression and Randomness - Part 2

In Part 1 we took a look at compression and encryption of text data with the aim of illustrating why compression should be done prior to encryption. A natural follow up is to try similar things on binary data and see what we find.

Encryption, Compression and Randomness - Part 1

One often comes across situations where data has to be compressed for size reduction and also encrypted for security. But should you first compress and then encrypt ? Or should it be done in reverse i.e. encrypt and then compress ?