Problem:  Have you ever wanted to talk to one of your buddies, but keep getting interrupted by other people Instant Messaging you?

Solution: To chat with someone while you are signed off you need to Directly Connect to them.  This is done by clicking on the "Connect to Send IM Image" icon in the IM window toolbar:

Once you and your buddy have established a Direct Connection, leave the chat window open and close AIM.  Your screen name will sign off, but you will still be able to chat with your buddy as long as you have the IM window open.

Notes: You can Directly Connect with as many buddies as you want to talk to while signed off.