Suppress comments from private page in sidebar

I’ve set up a couple of pages as password protected pages. I know how to suppress them from the listing of pages on my blog but when I comment to one of the pages, which I’ve done ad nauseum while testing the comment form, they are listed in the “recent comments” list on the sidebar. Since these are private pages, I’d rather not list them since that alerts visitors of the site to these pages…

Is there a way to suppress all comments made to a certain page from that recent comment list (or is there a plugin/widget that would allow me to do that)?