  We define a class of numerical semigroups S, which we call Castelnuovo
semigroups, and study the subvariety $M^S_{g,1}$ of $M_{g,1}$ consisting of
marked smooth curves with Weierstrass semigroup S. We determine the number of
irreducible components of these loci and determine their dimensions. Curves
with these Weierstrass semigroups are always Castelnuovo curves, which provides
the basic tool for our argument. This analysis provides examples of numerical
semigroups for which $M^S_{g,1}$ is reducible and non-equidimensional.
