Comment Delete for person who wrote comment

I have a muti-user wordpress environment. I would like a registered user who wrote a comment to be able to delete their own comment. I have disabled the ‘edit’ button because I don’t want the author of the post to see the commentors IP, email etc for privacy reasons.

So from the main blog, I would like the delete/trash link to be available on the comments a person wrote, and ideally also for the author of the post so they can better moderate the comments.