  We describe the moduli space G^r_d of triples consisting of a curve C, a line
bundle L on C of degree d, and a linear system V on L of dimension r. This
moduli space extends over a partial compactification {\tilde M_g} of M_g inside
{\bar M_g}. For the proper map h : G^r_d --> \tilde M_g, we compute the
push-forward on Chow 1-cocyles in the case where h has relative dimension zero.
As a consequence we obtain another counterexample to the Harris-Morrison slope
conjecture as well as an infinite sequence of potential counterexamples.
