Drainage networks generated with a simulation model based on the scaling relationship between slopes and areas were found to have total energy expenditure values very near the minimum value of optimal channel networks. Using this model to grow networks inside the boundaries of real basins, it is shown that the drainage networks identified with the aid of digital elevation maps in such basins tend to organize themselves in configurations that minimize total energy expenditure. The role of perturbations in the search for configurations with lower energy and the existence of unstable equilibrium landscapes are also examined.