All inversion procedures based on the single scatter (Born) model proposed in recent years possess two outstanding drawbacks which appear to be inherent to this approach. The first drawback is the unavoidable need to make an a priori choice of the ‘background’ problem. It is the reconstruction of the perturbation about this background that is subsequently sought. A successful outcome of the inversion sequence depends crucially on this initial decision. Although useful clues relevant to the background selection may, at times, be available, they are not an integral part of the Born inversion sequence. A second unfortunate feature of the Born inversion is the existence of mechanisms that give rise to error accumulation with range and to ‘scaling’ errors. The inversion sequence proposed in this paper seems to overcome the above deficiencies and to provide more accurately reconstructed results. The present scheme proposes a definite and unique choice of the background, namely, a WKB reference. This z dependent reference, although more complicated than the constant background, ordinarily selected for the single scatter model, can still be handled. Since the WKB background ensures correct relative phase (time delay) relations, it also seems to overcome the ‘scaling’ and error accumulation problems, which can be backtracked to ‘phase’ errors in the background (incident and backscattered) wave.