Over the last decade the scholarship on judicial politics has increasingly emphasized the strategic aspects of decision making in the United States Supreme Court. This scholarship, however, has struggled with two significant limitations—the restriction to unidimensional policy spaces and the assumption of binary comparisons of alternatives. These two assumptions have the advantage of implying stable, predictable outcomes, but lack a sound theoretical foundation and assume away potentially important aspects of strategic behavior on the Court. In this article, we identify institutional features of the Court that, under certain conditions, allow us to relax these two assumptions without sacrificing stable, predictable policy outcomes. In particular, we formalize the “part-by-part” opinion voting used by the justices, a feature that, together with separable preferences over policy issues, implies stable policy outcomes around the issue-by-issue median of the justices.