K-homology is the dual theory to K-theory. The BD (Baum-Douglas) isomorphism of Kasparov K-homology and K-cycle K-homology can be taken as providing a framework within which the Atiyah-Singer index theorem can be extended to certain non-elliptic operators. This talk will consider a class of non-elliptic differential operators on compact contact manifolds. These operators are in the Heisenberg calculus and have been studied by a number of mathematicians. Working within the BD framework, the index problem will be solved for these operators. Corollaries are solutions of the related equivariant and families index problems. This is joint work with Erik van Erp.