This paper deals with the design of a sliding perturbation estimator (SPE) with an improved adaptation law for the upper bound on the norm of perturbation. The proposed SPE, referred to as IMP-Based SPE, is based on the internal model principle and can thus achieve robust asymptotic perturbation estimation whereas the conventional SPE leads to nonzero estimation error to a time-varying perturbation. Besides, while the conventional SPE needs a switching gain greater than the magnitude of an unknown perturbation, the proposed IMP-Based SPE design releases this constraint and requires only a small switching gain as compared with the conventional design, further alleviating the chattering phenomenon. Moreover, in contrast with the previous bound estimation law that inevitably yields a non-decreasing switching gain, an improved estimation law is proposed to reduce the switching gain and thus the chatter whenever appropriate. The effectiveness of the proposed scheme is demonstrated through experimental studies of the track-following system of an optical disk drive suffering from significant disk runout.