The celebrated CLEAN algorithm has been the cornerstone of deconvolution algorithms in radio interferometry almost since its conception in the 1970s. For all its faults, CLEAN is remarkable in two regards viz. speed and its ability to accurately model point sources. In this talk, we demonstrate how the same assumptions that afford CLEAN its speed can be used to accelerate more sophisticated deconvolution algorithms. In particular, we approximate the Hessian of the likelihood function as a convolution with the point spread function and use this approximation to develop an effective preconditioner for a proximal gradient based imaging algorithm. The resulting algorithm, dubbed pre-conditioned forward-backward clean (pfb-clean), is implemented using forward-backward iterations and is particularly suited to imaging radio interferometric data in the regime where the data size is much larger than that of the image.