  Motivated by S-duality modularity conjectures in string theory, we define new
invariants counting a restricted class of 2-dimensional torsion sheaves,
enumerating pairs $Z\subset H$ in a Calabi-Yau threefold X. Here H is a member
of a sufficiently positive linear system and Z is a 1-dimensional subscheme of
it. The associated sheaf is the ideal sheaf of $Z\subset H$, pushed forward to
X and considered as a certain Joyce-Song pair in the derived category of X. We
express these invariants in terms of the MNOP invariants of X.
