Strong-field ionization of atoms or ions by short laser pulses is analyzed by means of the eikonal perturbation theory.This newly developed approach in the first order with respect to the binding potential avoids a singularity at its center and,in contrast to the ordinary eikonal approximation(the so-called Molière-Glauber eikonal for the Schr"odinger equation),it allows to treat rescattering phenomena in terms of quantum trajectories.