Variable density sampling is now commonly used in advanced imaging methods. However, due to ill conditioning, reconstruction can take hundreds of iterations, limiting its clinical application. One effective heuristic to accelerate convergence is the use of density compensation, but it is known to increase reconstruction error. An alternative is to use preconditioners, but existing preconditioners increase computation by performing additional image convolutions. Our goal here is to accelerate iterative reconstruction convergence without compromises. We propose a k-space diagonal preconditioner, without compromising reconstruction error, or computation. We demonstrate on datasets that reconstructions with the proposed preconditioner converge at around 10 iterations.