  We consider random walks in a random environment of the type p_0+\gamma\xi_z,
where p_0 denotes the transition probabilities of a stationary random walk on
\BbbZ^d, to nearest neighbors, and \xi_z is an i.i.d. random perturbation. We
give an explicit expansion, for small \gamma, of the asymptotic speed of the
random walk under the annealed law, up to order 2. As an application, we
construct, in dimension d\ge2, a walk which goes faster than the stationary
walk under the mean environment.
