Try the "Contact Staff" mod. It requires users to both use the drop-down menu to select a staff member and to complete a random CAPTCHA. Currently it uses only images of numerals; however, the default is 8 characters. It could be changed to use alpha-numerics.
If you wanted to help reduce spam from newly registered accounts, could also incorporate something like I did for this post.

It will be more difficult for an automated spam script to do it, but it would still be possible with a good bit of effort. Most spammers don't want to put that much into it, though, due to the law of diminishing returns.
What it can do is prevent newly registered (or not registered) people from using the form at all (if you choose to incorporate that function) and force the spammers to manually use the form. That's too much like work for most of them.

Zenfor, without knowing more about your specific situation, it's tough to be certain, but this may be helpful.

http://sourceforge.net/projects/internetcaptcha/?source=directory