Adaptive modulation with the goal of minimizing the average transmit power is investigated. This is the dual problem of the well-known problem of maximizing the average spectral efficiency. This is desirable in power limited systems such as mobile and sensor networks. Two main cases are considered: adapting only transmit power and adapting only rate. Appropriate expressions for rate or power control policies are derived for different cases. For rate adaptation, we consider both continuous and discrete rate policies. Then, we will apply these methods to a special case of M-QAM modulation over Rayleigh fading channel. We will show that by using rate or power adaptation schemes, between 7 dB and 18 dB power gain can be saved over nonadaptive methods for typical values of spectral efficiency