  The locus of genus-two curves with n marked Weierstrass points has
codimension n inside the moduli space of genus-two curves with n marked points,
for n<=6. It is well known that the class of the closure of the divisor
obtained for n=1 spans an extremal ray of the cone of effective divisor
classes. We generalize this result for all n: we show that the class of the
closure of the locus of genus-two curves with n marked Weierstrass points spans
an extremal ray of the cone of effective classes of codimension n, for n<=6. A
related construction produces extremal nef curve classes in moduli spaces of
pointed elliptic curves.
