We solve the part of the Donaldson-Thomas theory of Calabi-Yau
threefolds which comes from super-rigid rational curves. As an
application, we prove a version of the conjectural
Gromov-Witten/Donaldson-Thomas correspondence of [MNOP] for
contributions from super-rigid rational curves. In particular, we
prove the full GW/DT correspondence for the quintic threefold in
degrees one and two.