When Orthogonal Frequency Division Multiplexing (OFDM) is used to transmit information over a frequency selective channel, it is convenient to vary the power and the number of bits allocated to each subcarrier in order to optimize the system performance. In this paper, the three classical problems of transmission power minimization, error rate minimization and throughput maximization are investigated in a unified manner. The relations existing among these three problems are clarified and a precise definition of optimum system is given. A general and rigorous way to extend the solution of any of the three problems in order to obtain the solution of the other two is presented. This result is used to devise an efficient algorithm for the error rate minimization.