The recently introduced Rational Function (RF) model permits a linear solution of epipolar geometry and lens distortion from image correspondences for a very general class of lenses. In this paper we show that the model also permits a very elegant form of the plumbline constraint which allows uncalibrated correction of lens distortion from a single image containing lines known to be straight in the world. We show how this may be expressed as a factorization problem, and discuss its behaviour with noisy data. We also introduce a simple reduced parametrization of the RF model which again models a range of existing lenses. Because the RF model provides a very simple form for the distorted lines, nonlinear minimization can compute the Sampson distance to the distorted lines, allowing fast and accurate estimation of the RF model even from noisy images.