The Strominger system is a system of PDEs derived by Strominger in his
study of compactification of heterotic strings with torsion. It can be
thought of as a generalization of Ricci-flat metrics on non-Kähler
Calabi-Yau 3-folds. We present some new solutions to the Strominger
system on a class of noncompact 3-folds constructed by twistor
technique. These manifolds include the resolved conifold
Tot(O(-1,-1)->P1) as a special case.