Traffic is believed to organize itself by minimizing user’s travel cost (travel time is used as cost very often). Almost all the analytical and numerical work in the last 50 years has concentrated on travel cost and the assumption that costs are always an increasing function of demand. With fuel consumption, this is no longer true, since there is typically an optimum speed where fuel consumption and emission production is minimized. This paper explores some of the implications when using fuel consumption as an objective function for achieving an user equilibrium traffic state. It turns out, that this leads to multiple solutions (multiple equilibria) and sometimes counter-intuitive behavior, which makes it unlikely that such a scheme that minimizes fuel consumption alone will ever be implemented in real systems.