The most efficient signal edge-preserving smoothing filters, e.g., for denoising, are non-linear. Thus, their acceleration is challenging and is often done in practice by tuning filters parameters, such as increasing the width of the local smoothing neighborhood, resulting in more aggressive smoothing of a single sweep at the cost of increased edge blurring. We propose an alternative technology, accelerating the original filters without tuning, by running them through a conjugate gradient method, not affecting their quality. The filter non-linearity is dealt with by careful freezing and restarting. Our initial numerical experiments on toy one-dimensional signals demonstrate 20x acceleration of the classical bilateral filter and 4-5x acceleration of the recently developed guided filter.[http://arxiv.org/abs/1509.01514]