In this paper, a new power allocation and bit loading policy is defined for those systems working with a preselected binary channel code and specific bit error rate (BER) requirements. It consists on the maximization of the spectral efficiency with a constraint on the average mutual information per coded bit (bit MI), exploiting the relationship of the bit MI with the BER and the code rate. An irregular modulation approach is employed in order to express the policy as a convex optimization problem, solved without the need of greedy algorithms. Results are compared with those obtained with other algorithms in the literature.