  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 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.
