The problem investigated is that of minimizing an integral of the vth power of the magnitude of the system error, for a double-integrator plant with bounded control. It is known that the problem may be reduced by means of dimensional analysis to the determination of a single parameter in the control law. Methods of computing with high precision the optimal value of this parameter are studied in the present paper. It is also shown that for certain values of v the optimal controller becomes the same as the time-optimal controller.