Thanks for your reply.
OK, I've worked out what to do to sync sent messages both ways:
I have to go to the 'Sent Messages' folder (not the the 'Sent'), and mark it 'Sync with [ Sent ] folder' I then have to open the spanner and click the IMAP Push Box. Hurray!
It's not so important, but I still cannot sync the Deleted messages folder. Is there any way to do that (The option for Deleted Messages is 'Sync with [ Deleted ] folder', but the folder for deleted messages on iCloud is called Trash.