Blind deconvolution is known as a challenging low-level vision problem due to the diverse blur scenarios in real-world imaging. Another attempt is made with critical thoughts on existing image priors for nonparametric blur kernel estimation, proposing an alternative approach to blind deconvolution via complementarily structure-aware image smoothing (CSIS). Similar to most state-of-the-art blind deblurring methods, the proposed approach partly builds on the naïve L0-based sparse model, but the core contribution here is to additionally advocate a type of redescending potential (RDP) functions as a more elegant way for boosting blind deblurring. With the RDP element, the new approach is capable of easily achieving the discrimination between clear and blurred images. Meanwhile, the performance of the proposed method can be better ensured due to the complementary smoothing behavior induced by the RDP functions. Specifically speaking, it is known that L0-based smoothing plays a critical role in pursuing salient step-edges from blurry images especially in the early period of blur kernel estimation, whereas the RDP-based smoothing is found particularly significant in the later stage when the fine pursuit of salient roof-edges or ramp-edges are dominantly critical for more precise and robust kernel estimation. In this sense, the proposed CSIS-based blind deblurring algorithm is more intuitive than previous L0-based methods. Not only that, numerous experimental results on benchmark blurred images, no matter synthetic or realistic, also demonstrate the comparable or even better performance of the proposed approach in terms of both effectiveness and robustness.