We present a highly efficient blind image 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 principle-based way. In this sense, we present a novel procedure to design the approximate inverse of a filter and make only use of re-applications of the filter itself. To estimate image blur in natural images we introduce a simple yet robust algorithm based on empirical observations about the distribution of the gradient in sharp images. Our experiments show that, in the context of mild blur, the proposed method outperforms traditional and modern blind deconvolution methods and runs in a fraction of time. We finally show that the method can be used to blindly correct blur before applying an out-of-the-shelf deep super-resolution model leading to superior results than other highly complex and computational demanding methods. The proposed method can estimate and remove mild blur on a 12Mp image on a modern mobile phone device in a fraction of a second.