It is shown: (a) the core conservatives justices now on the Supreme Court (identified as White, Rehnquist, O'Connor, Scalia and Kennedy) are preoccupied with the problem of the fit between their rulings and the sources of law and with the ideal of predictability; (b) a new jurisprudential approach developed by Justice Scalia is gaining acceptance amongst them; (c) Scalia's reasons for rejecting the neo-conservative doctrine that the intentions of the Constitution's Framers should be the only legitimate point of reference in constitutional cases are sound; (d) his suggestions for an alternative theory offer a defensible way forward which has advantages over competing orientations.