Micromagnetic studies have been performed to find optimum shape of hysteresis loop in a single-layered perpendicular medium for ultrahigh density recording. A good index that was inversely proportional to signal-to-noise ratio (SNR) was developed. By using this index, we found the optimum loop shape should have terms of the ratio of nucleation field to coercivity within -0.4 to -0.6, the loop slope within 2 to 4, and the ratio of grain thickness to grain diameter larger than 2.5.