  We consider discrete one-dimensional Schr\"odinger operators with strictly
ergodic, aperiodic potentials taking finitely many values. The well-known
tendency of these operators to have purely singular continuous spectrum of zero
Lebesgue measure is further elucidated. We provide a unified approach to both
the study of the spectral type as well as the measure of the spectrum as a set.
We apply this approach to Schr\"odinger operators with Sturmian potentials.
Finally, in the appendix, we discuss the two different strictly ergodic
dynamical systems associated to a circle map.
