  We consider a random walk in an i.i.d. non-negative potential on the
d-dimensional integer lattice. The walk starts at the origin and is conditioned
to hit a remote location y on the lattice. We prove that the expected time
under the annealed path measure needed by the random walk to reach y grows only
linearly in the distance from y to the origin. In dimension one we show the
existence of the asymptotic positive speed.
