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Two approaches, i.e., a diffraction model considering Fresnel reflection and a paraxial beam propagation method are utilized to optimize the design of wedge-shaped lensed fibers for coupling between laser diodes of highly asymmetrical beam and single-mode fibers. It is demonstrated for the first time that, in contrast to the prevailing view, the non-Gaussian fiber-mode shape modification by the wedged fiber tip greatly reduces the coupling efficiency when the wedge angle is relatively large, while the Fresnel reflection is found to play an insignificant role. The fundamental cause of the non-Gaussian shape effect is fully explored and, consequently, a novel design is proposed to suppress this effect and increase coupling efficiency. Moreover, the novel design is relatively simple, and it does not complicate the fiber tip fabrication process.