The purpose of this paper is to investigate projection methods for the iterative computation of partially balanced reduced order systems. This approach is both completely automatic once an error tolerance is specified and yields an error bound. This is to be contrasted with existing projection methods, namely PVL (Padé via Lanczos) and rational Krylov, which do not satisfy these properties. Our approach is based on the computation and appoximation of certain system grammians and in particular on the cross grammian.