Lee helm in light winds
I'm pretty new to sailing, so I apologize if the following doesn't make much sense:
I'm getting lee helm in very light winds (3-5 knots or so). In order to maintain a close hauled course I have to keep the tiller about 30 degrees to lee. This, I think, slows down the boat even more. If I let the tiller go, the boat falls off to a beam reach.
I've read a little bit about Center of Effort (CE) and Center of Lateral Plane (CLP), and how a large lead may cause lee helm. I've also read about tinkering with the mast (basically leaning it back a bit) to correct lee helm. Problem is that I'm renting Flying Scots and I definitely don't want to mess with the mast.
Other than messing with the mast, what can I do to deal with lee helm in light winds? Would raising the centerboard help? What else?
Thanks for any thoughts.

Comments
Just thought about this issue some more.
I know that raising the rudder creates weather helm.
Thanks for the suggestion.