We propose multiple-input multiple-output (MIMO)transmitter power allocation which takes dissipation in the power amplifiers into account. We derive the equations of the generalproblem with full channel state information (CSI), discuss its challenges, and supply solutions in two special cases, namely fora multiple-input single-output channel with a linear beamformer constraint, and for a parallel MIMO channel. The proposed algorithms show substantial gains in terms of rate and total consumed power compared to previous state of the art over awide range of parameter settings, and have low computational complexities.