Convenient shortcut to push delete current branch?

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?