Twitter SUCKS! It has no way to automatically eliminate the huge amounts of Direct Message Spam that is sent. Yes, I know you can tighten down the screws and manually approve who follows you but that’s not a solution. It works like this: you Follow someone and they use a “Bot” to automatically send you a Direct Message (DM). Not everyone does this but in my informal calculations while helping my GEEK Princess 
named Cathy, around 75% of these DMs are Spam. They are easy to spot since the Bot stuff never uses your full real name on Twitter.
Stupid Spam and every kind of Scam deal you could imagine. It would have taken hours to eliminate her Direct Message Spam using Twitter. Over 1K in just a few weeks. Each message must be eliminated one by one. The solution is brutal but it works. Use Firefox (did not work in IE 7) and DM Whacker and they were all nuked in about 30 seconds. Unfortunately, some nice people get WHACKED but you can set up a second Twitter account with tight options and tell your real deal network to respond to this account.