Yeah, it is Swing...sorry, didn't notice the specific forum. :-) Just writing back to say that I found my answer. It's not coding, it's framework. I used the Scrollable interface to specify the required dimensions in my custom component.
I wasn't familiar with this interface, and I'm a little dissapointed that "Java Swing" doesn't cover it. But, they did mention it...and the rest was a piece of cake.