how to keep folders in sync over the Internet ("long-distance", not LAN)? I mean *sparingly*

So far I have been using rsync for this purpose, but there is still space for optimizations.

If I locally rename a big file, next time my "rsync -vaz --delete-after" will copy the file using the new name and remove it using its old name. I would actually prefer to see the file getting renamed remotely.

Posted this issue on the rsync user mailing list [link].
In response to that, I received a message pointing me to the "should" tool [link].