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We examine adaptive modulation schemes for flat-fading channels where the data rate, transmit power, and instantaneous BER are varied to maximize spectral efficiency, subject to an average power and BER constraint. Both continuous-rate and discrete-rate adaptation are considered, as well as average and instantaneous BER constraints. We find the general form of power, BER and data rate adaptation that maximizes spectral efficiency for a large class of modulation techniques and fading distributions. The optimal adaptation of these parameters is to increase the power and data rate and decrease the BER as the channel quality improves. Surprisingly, little spectral efficiency is lost when the power or rate is constrained to be constant. Hence, the spectral efficiency of adaptive modulation is relatively insensitive to which degrees of freedom are adapted.