I've explained my solution about the Supreme Court on here before, but let's go once more.
The Supreme Court should not be a permanent set of justices but a rotating cast. Each year draw one judge at random from each circuit to be the SC for the year. Once a judge serves he can't be selected again for a number of years. The justices that grant certiorari would do so for the next year's court, without knowing who the next justices will be. This would serve to make the court less partisan, less political, and adhere closer to established precedent.