In this letter we focus on the power allocation in multicarrier modulation system (MCM). We consider two non iterative algorithms of adaptive power loading (APL). The first of them minimizes the average power of the system transmitter and ensures the preset average bit-error rate (BER) and the second provides decreasing of the average transmitting power subject to the given values of demanded BER and the outage probability. The considered algorithms may be used for power-efficient management of the up-link in cellular communication, where mobile terminals use rechargeable batteries, or of the downlink in satellite communication with solar power source of a transponder. Performance analysis of the adaptive MCM (AMCM) systems supported by computer simulation for the case of the m-Nakagami fading and additive white Gaussian noise in the forward and backward channels is presented. Evaluation of the average power gain (APG) of the considered APL strategies and its comparison with uniform power loading strategy, shows that APG depends on average signal to noise ratio (ASNR) in the system sub channels and can reach 20 dB.