Redmine

I'd like to install Redmine to https://secure.example.com/redmine/ but it seems I'm limited to installing it to root virtual directory only.
The requirement is that the connection is secure (https), but I don't want to have to purchase an extra security certificate to just use Redmine.

I've tried substituting strings on the fly but it gets pretty messy.
A possible fix is pretty obvious: set a global variable in the config file, then include it for every URL in the system. Of course this would need to apply to AJAX calls as well as to normal URLs.