An approximate formula is given by which the potential Q(x) can be recovered with any accuracy if only the scattering data of the Schrödinger operator -Δ + Q(x) is known for some sufficiently high energy value k. Thus the scattering data for all k around k = ∞ is not needed in order to get a good approximate value for the potential. The main tools for the proof are an asymptotic formula for the S-matrix [Y. Saitō, J. Math. Phys. 25, 3105 (1984)] and the spectral decomposition theorem for the Schrödinger operator -Δ + Q(x) based on the limiting absorption principle. © 1986 American Institute of Physics.