  Let K be a tame knot with irreducible exterior M(K) in a closed, connected,
orientable 3--manifold Sigma such that pi_1(Sigma) is cyclic. If infinity is
not a strict boundary slope, then the diameter of the set of strict boundary
slopes of K, denoted d_K, is a numerical invariant of K. We show that either
(i) d_K >= 2 or (ii) K is a generalized iterated torus knot. The proof combines
results from Culler and Shalen [Comment. Math. Helv. 74 (1999) 530-547] with a
result about the effect of cabling on boundary slopes.
