  The purpose of this article is to study compactness of the complex Green
operator on CR manifolds of hypersurface type. We introduce (CR-P_q), a
potential theoretic condition on $(0,q)$-forms that generalizes Catlin's
property (P_q) to CR manifolds of arbitrary codimension. We prove that if an
embedded CR-manifold of hypersurface type satisfies (CR-P_q) and (CR-P_{n-1-q})
and is of real dimension at least five, then the complex Green operator is a
compact operator on the Sobolev spaces $H^s_{0,q}(M)$, if $1\leq q \leq n-2$
and $s\geq 0$. We use CR-plurisubharmonic functions to build a microlocal norm
that controls the totally real direction of the tangent bundle.
