Ultimate gains and ultimate periods have long been used to tune PI/PID controllers since the Ziegler-Nichols tuning. Recently, very simple analytic equations for ultimate gains and ultimate periods by approximating the arctangent function have been presented, which can be used to obtain simple tuning rules. Here, by applying the Routh stability method and phase-optimal approximations of the time delay term, we present analytic expressions of ultimate parameters that are as simple as the existing ones, showing better accuracy.