Require that Supreme-Court Justices, including the Chief Justice be confirmed by a two-thirds vote of the Senate, not a simple majority.
Of the current Supreme-Court justices, three failed to get a two-thirds confirmation vote. Shown with the votes, and the appointing President, they are:
Clarence Thomas 52–48 George H. W. Bush
Samuel Alito 58–42 George W. Bush
Elena Kagan 63–37 Barack Obama