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We experimentally investigate and characterize the improvement in thresholding capability of a compact highly Ge-doped nonlinear interferometer-based all-optical thresholder using optical offset spectral filtering. The thresholder we study has an in-loop nonlinearity requirement lower than that of a classical nonlinear loop mirror scheme. Therefore, only 15 m of nonholey silica-based fiber is used as a nonlinear element. Although the nonlinear interferometer-based thresholder has been useful for signal regeneration and thresholding, it has several limitations, including severe pulse distortion due to pulse bifurcation at high input powers and a fixed power transfer function. In this paper, we propose and demonstrate the use of offset spectral filtering at the output of this Ge-doped low nonlinearity interferometer-based thresholder to adjust the power transfer function and thresholding slope, as well as reducing pulse distortion due to pulse bifurcation. To the best of our knowledge, this is the first experimental demonstration of power transfer function tailoring, which makes the thresholder more flexible and allows customization of thresholding parameters in meeting requirements in various systems.