Tmux Part 4: Vim Integration

When I use Vim from within tmux, the delete key (or Ctrl-H) sends a ^? character instead of a backspace, i.e.:

YOU WILL BE DELETED^?^?^?^?^?^?^?^? 

This doesn’t happen elsewhere in tmux, not does it happen in Vim outside tmux. This is surely related to my other problem with Ctrl-H failing to switch panes. As was the case there, toggling the Delete Sends Ctrl-H setting has no effect here. Any idea what the ^? is or what’s wrong with my Ctrl-H?