In blind deblurring, the goal is to recover a latent sharp image from its blurred version when the blur kernel is unknown. In this case, natural image priors often lead to intractable algorithms or failures if used with maximum a posteriori (MAP) estimation. Therefore, the ruling approach is to start with estimating only the kernel, and then use it to recover the latent image via non-blind deblurring. While many blind deblurring works focus on the kernel estimation, we consider the second phase, where we build on the recently proposed Iterative Denoising and Backward Projections (IDBP) strategy. The proposed method uses an automatic parameters tuning mechanism, which can tune the parameters differently for each kernel and image, contrary to other deblurring algorithms that are restricted to a uniform tuning in the blind-deblurring setting. We demonstrate the advantages of our method over widely used deblurring algorithms.