GIT and the current -stable

Good day.

Stumbling around with git here. I'd like to use git to efficiently track the 
  current -stable as well as -current. Say, my local tree is a clone of 
Linus current:

git clone \ git://git.kernel.org/pub/scm/linux/kernel/git/torvalds/linux-2.6.git local

I then branch off a 2.6.20 branch:

cd local git checkout -b v2.6.20 v2.6.20

to now update to the current -stable I could do:

git pull \ git://git.kernel.org/pub/scm/linux/kernel/git/stable/linux-2.6.20.y.git

each time that a new -stable is released. Rather though, I'd like a simple "git pull" to do this while on this branch while a "git pull" while back on the master branch pulls from the originally cloned Linus repo again.

Is this possible? Do I want it to be? Comments like "work like this instead" welcome as well; figuring out what the heck it is that I want from git seems to be one of the most difficult questions to answer...

Currently using git 1.5.0.4.

Rene.