This paper studies an energy efficient design of precoders for point-to-point multiple-input-multiple-output (MIMO) orthogonal frequency-division multiplexing (OFDM) systems. Differently from traditional approaches, the optimal power allocation strategy is studied by modelling the circuit power as a rate-dependent function. We show that if the circuit power is a constant plus an increasing and convex function of the transmission rate, the problem of minimizing the consumed energy per bit received can be reformulated as a convex fractional program and solved by means of a bisection algorithm. The impact of the some system parameters is investigated either analytically or by means of computational results.