Make Synchronize Delete Deleted Files

I run synchronize both from a script.
It works like a dream.
The only problem I'm having is that if I delete a file at one end (local or server) it replaces the file with the copy at the other end.
I've tried it with synchdelete on and off.
How can I synchronize using a script and be able to delete things?

See my answer here. Please, do not double-post.