Help! Site Under Major Mail Bomb Attack

A site I recently moved to a new server is under some kind of mail bombing attack using what appears to be a random name generator. The emails are coming from numerous IP's, most of which are outside the US. I have DirectAdmin set to drop email addresses that are not addressed to a known user and I have Exim set to reject spam based on RBL. According to my exim logs I'm rejecting over 10,000 emails per hour. While I'm not getting these emails it's a pure waste of bandwidth and resources.

Anyone have any recommendations on how I can stop this?

Dave

 

 

 

 

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