for complex smooth threefolds, there are enumerative theories of curves defined using sheaves, such as donaldson-thomas (dt) theory using ideal sheaves and pandharipande-thomas (pt) theory using stable pairs. these theories are conjecturally related among themselves and conjecturally related to other enumerative theories of curves, such as gromov-witten theory. the conjectural relation between dt and pt theories is known only for calabi-yau threefolds by work of bridgeland, toda, where one can use the powerful machinery of motivic hall algebras due to joyce and his collaborators. bryan-steinberg (bs) defined enumerative invariants for calabi-yau threefolds $y$ with certain contraction maps $y\rightarrow x$. i plan to explain how to extend their definition beyond the calabi-yau case and what is the conjectural relation to the other enumerative theories. this conjectural relation is known in the calabi-yau case by work of bryan-steinberg using the motivic hall algebra. in contrast to the dt/ pt correspondence, we manage to establish the bs/ pt correspondence in some non-calabi-yau situations.