Microlensing can provide a useful tool to probe binary distributions down to low-mass limits of binary companions. In this paper, we analyze the light curves of eight binary-lensing events detected through the channel of high-magnification events during the seasons from 2007 to 2010. The perturbations, which are confined near the peak of the light curves, can be easily distinguished from the central perturbations caused by planets. However, the degeneracy between close and wide binary solutions cannot be resolved with a 3σ confidence level for three events, implying that the degeneracy would be an important obstacle in studying binary distributions. The dependence of the degeneracy on the lensing parameters is consistent with a theoretical prediction that the degeneracy becomes severe as the binary separation and the mass ratio deviate from the values of resonant caustics. The measured mass ratio of the event OGLE-2008-BLG-510/MOA-2008-BLG-369 is q ~ 0.1, making the companion of the lens a strong brown dwarf candidate.