The widely-used LMS algorithm for coefficient updates in adaptive (feedforward/decision-feedback) equalizers is found to be suboptimal for ASE-dominant systems but various coefficient-dithering approaches suffer from slow adaptation rate without guarantee of convergence. In view of the non-Gaussian nature of optical noise after the square-law optoelectronic conversion, we propose to apply the higher-order least-mean 2Nth-order (LMN) algorithms resulting in OSNR penalty which is 1.5–2 dB less than that of LMS. Furthermore, combined with adjustable slicer threshold control, the proposed equalizer structures are demonstrated through extensive Monte Carlo simulations to achieve better performance