We will consider the alpha' expansion of the Strominger system derived from heterotic string compactifications to an N=1 supersymmetric effective field theory on four dimensional Minkowski space. We discuss the alpha' expansion and show that the conformally balanced condition is required by supersymmetry to second order in the alpha' expansion. We also study the Bianchi identities to second order and show that the equations of motion are satisfied to this order if the manifold admits an instanton connection. This proves that the well known result to first order extends to second order in alpha'. We then consider the moduli space of the supersymmetry solutions and show that the Bianchi identity can be used to determine the alpha' corrections to the geometry in terms of the zeroth' order background solution.