This paper considers the performance of time-domain power-allocation schemes with average and peak power constraints and proposes a constant-power allocation (CPA) scheme. In a Nakagami-m fading environment, an exact closed-form expression for the ergodic capacity of the proposed CPA scheme is derived, and the effect of the fading parameter m on the performance degradation due to a peak power constraint is investigated. The proposed scheme shows a near-optimum performance within 5% of the optimal capacity and provides a noticeable performance improvement as it reduces the peak-to-average power ratio (PAPR) with a signal-to-noise ratio (SNR) gain of approximately 8.5 dB while also mitigating the intercell interference in the uplink.