Is there any way to block ZERO feedback bidders?

I try to remember we were all zero feedback bidders at one time, but way back when I was new, ebay was different (better and more fun)....I disclose no zero feedback bidders in my auctions. But when they make an attempt to contact me and ask me if they can bid and that they really want the item I allow it. The fact that they asked before just bidding means alot to me, and usually shows their integrity. Some of them have become regular buyers and some of my favorites.:P