Is there a way to trim old SHAs from a git tree (so it's not so large)?

After doing a "make mrproper" in my Linux git tree, the result is still 1.1GB of files. Compare that with just the tarball, which is just one-forth the size.

Is there a way to "trim away" old commits from the repository, so that it just 
doesn't take up that much space?  I don't care about any commits made in 2005. 
  As long as I can still do "git pull" from the source repo to update mine, 
that's good enough.