Android - How do I delete a draft message (SMS)?

just clear the text of the draft message, and it will automatically disappear

Just figured this one out having had the same problem myself (HTC Desire HD, Android 2.2)....

From the "All Messages" view, press the Menu button. A "Drafts" icon appears (a floppy disk icon) - press that, and it takes you to a view of all your drafts.

Press & hold a draft message to View/Delete or press the Menu button again & select Delete Drafts to go to a view where you can bulk mark the drafts you want to delete.

Hope that helps!

Have you tried pressing and holding on the text of the draft message and then using the context menu to delete that single draft message?