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We present a highly efficient blind restoration method to remove mild blur in natural images. Contrary to the mainstream, we focus on removing slight blur that is often present, damaging image quality and commonly generated by small out-of-focus, lens blur, or slight camera motion. The proposed algorithm first estimates image blur and then compensates for it by combining multiple applications of the estimated blur in a principled way. To estimate blur we introduce a simple yet robust algorithm based on empirical observations about the distribution of the gradient in sharp natural images. Our experiments show that, in the context of mild blur, the proposed method outperforms traditional and modern blind deblurring methods and runs in a fraction of the time. Our method can be used to blindly correct blur before applying off-the-shelf deep super-resolution methods leading to superior results than other highly complex and computationally demanding techniques. The proposed method estimates and removes mild blur from a 12MP image on a modern mobile phone in a fraction of a second.