A novel discrete-valued model-predictive control (DVMPC) algorithm termed DVMPC2 for the position control of pneumatic actuators using inexpensive on/off valves is presented. DVMPC2 includes a more flexible cost function, an improved prediction strategy, and other improvements. The actuator is a double-acting cylinder with two on/off solenoid poppet valves connected to each chamber. To reduce the switching frequency and prolong the valve life, DVMPC2 directly switches the valves when necessary, instead of using relatively high-frequency pulse-width modulation. Experimental comparisons are made with the state-of-the-art sliding-mode control (SMC) algorithm and the previous DVMPC algorithm. The comparisons are based on the five performance metrics: integral of time-weighted absolute error (ITAE), root mean square error (RMSE), overshoot (OS), steady-state error (SSE), and valve switches per second (SPS). The robustness is evaluated by increasing and decreasing the total mass of the moving components while keeping the controller parameters constant. The experimental results show that the proposed algorithm is superior to the previous DVMPC and outperformed SMC by a wide margin. Specifically, DVMPC2 reduced ITAE by 80%, RMSE by 52%, OS by 43%, and SPS by 20% relative to SMC. There was no clear winner in terms of SSE.