Convenient shortcut to push delete current branch?

[Robert Dailey <rcdailey.lists@gmail.com>]

For convenient pushing of current branch, git supports this syntax:

$ git push origin HEAD

This will push your current branch up. However, is there such a
shortcut for *deleting* the branch? The only goal here is to avoid
having to type the branch name in the push command. Normally I rely on
tab completion but we have tons of branches, all which start with some
prefix mixed with numbers, so it becomes cumbersome to rely on tab
completion. Ideally I'd like to be able to do:

$ git push --delete origin HEAD
$ git push origin :HEAD

Is there a syntax like this available?