In this work, we are concerned with power efficient communication techniques for wireless mobile devices. In this direction the effects of nonlinear amplifiers in communications systems are first studied, as they tend to consume a large fraction of available battery power. Next, a new information theoretic upper bound is proposed that takes into account power efficiency, and the bound achieving input distributions are analyzed and shown to be strikingly different than those that achieve channel capacity. Next, in order to examine methods to achieve the power efficient input distributions, results on shaping gains are restated, with particular emphasis on non-equiprobable signaling in two dimensions. With slight changes in classical techniques we are able achieve power efficient signaling schemes that reduce the wasted power from RF amplification. Finally, simulation results are shown to verify the savings in wasted energy obtained through the use of these power efficient signaling schemes.