We present a conformal deformation involving a fully nonlinear equation in dimension $4$, starting with a metric of positive scalar curvature. Assuming a certain conformal invariant is positive, one may deform from positive scalar curvature to a stronger condition involving the Ricci tensor. A special case of this deformation provides an alternative proof to the main result in Chang, Gursky \& Yang, 2002. We also give a new conformally invariant condition for positivity of the Paneitz operator, generalizing the results in Gursky, 1999. From the existence results in Chang \& Yang, 1995, this allows us to give many new examples of manifolds admitting metrics with constant $Q$-curvature.