We consider slotted ALOHA systems with a controlled output power level. The systems were proposed to improve the throughput performance by the capture effect. However widely used linear modulation systems have no capture effect, and a power level distribution dominates the performance in those systems. In this paper we consider linear modulation systems employing PSK. We introduce an average error probability of the highest power signal as a performance measure, and a uniform distribution is applied to the error probability analysis. Numerical results show the superiority of the systems with uniform distribution to a conventional slotted ALOHA in a heavy traffic condition. On the other hand, in a light traffic condition, the optimal power distribution which minimizes the error probability is obtained for 2-level ALOHA. We also propose the power level selection method to search the optimal power level. The validity of analytical results are confirmed by simulations.