Multiple domain names under one domain

I am running a Magento store and have decided to try creating another store view with a different domain.

I've gone into virtualmin and created an alias server, but maybe this isn't the right one.

I have www.domain1.com and would like www.domain2.com to work out of the same directories as www.domain1.com

Magento has the ability to listen to the incoming domain names and handle them appropriatly.

The issue right now is that if I type www.domain2.com, I get redirected to www.domain1.com

Is an alias server the right selection for what I'm trying to achieve?

Thanks,

SR