But wait. Surely you can already delete your saved searches?
Yeah, of course you can. But unfortunately there's a bug which means that you can't delete a search if there are no results for it. So if your search was for "Gordon Brown" (who he? Ed.), you're out of luck.
Twitter haven't seemed very interested in fixing it. Their suggested workaround is to write a tweet containing your search phrase. Great. Let the whole world know what you're searching for, why doncha?
Anyway, go and use it.