public/private posts

I’m having a bit of a problem, and I wonder if anyone can help me. I’m helping to set up a blog for a group I’m in. We want to be able to have both public and private posts. We want anyone to be able to see the public posts, but only people who are logged in to see the private posts. And we don’t necessarily want the public to know that there are private posts that they can’t see. Is there a way to do this? Thanks a lot.