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The problem of power loading in orthogonal frequency division multiplexing (OFDM)-based systems that provides minimization of the bit-error rate (BER) performance under a fixed transmit power (or equivalently minimisation of the transmit power under a fixed value of the BER) is addressed in this work. A lemma about inversion of subchannel power gains is proved and examples that exhibit its utility are presented. As a result, a non-iterative adaptive power allocation technique is derived. The algorithm combines the recently proposed ordered subcarrier selection method with 'subchannel inversion'. Compared with the original technique, such a combination provides a power gain that depends on the channel statistics.