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To recover a sharp version from a blurred image is a long-standing inverse problem. In this paper, we analyze the research on this topic both theoretically and experimentally through three paradigms: 1) the deterministic filter; 2) Bayesian estimation; and 3) the conjunctive deblurring algorithm (CODA), which performs the deterministic filter and Bayesian estimation in a conjunctive manner. We point out the weaknesses of the deterministic filter and unify the limitation latent in two kinds of Bayesian estimators. We further explain why the CODA is able to handle quite large blurs beyond Bayesian estimation. Finally, we propose a novel method to overcome several unreported limitations of the CODA. Although extensive experiments demonstrate that our method outperforms state-of-the-art methods with a large margin, some common problems of image deblurring still remain unsolved and should attract further research efforts.