Update EC2 AMI root drive

I have an EC2 AMI that I create instances from to be used to execute builds. I now need to modify this AMI because I need an additional program installed on it. What I want to do is make my AMI point at a different snapshot to use as its root drive (a snapshot with the new program installed) and things would be all well and good. But, I can't find a way to do this. Someone from Amazon on the forums said it's not possible, but I'm not so sure. So, I wanted to ask here.

I know I can just take the updated snapshot I want and create an entirely new AMI from it, but this results in a new AMI ID and now I need to go change the AMI ID which my scripts use to launch a new instance. I don't want to do this every time I realize I need a change to my AMI setup.