  Two new invariants that are closely related to Milnor's curvature-torsion
invariant are introduced. The first, the spiral index of a knot, captures the
minimum number of maxima among all knot projections that are free of inflection
points. This invariant is closely related to both the bridge and braid index of
the knot. The second, the projective superbridge index, provides a method of
counting the greatest number of maxima that occur in a given knot projection.
In addition to investigating how these invariants are related to the classical
invariants, we utilize them to determine all knots with curvature-torsion
invariant equal to 6 pi.
