<p>We are interested in improving validity results for the nonlinear Schrödinger (NLS) approximation beyond the natural time scale for completely integrable systems. As a first step, we consider this approximation for the Korteweg–de Vries equation with initial conditions for which the scattering data contain no eigenvalues. By performing a linear Schrödinger approximation for the scattering data, the error made by this approximation has only to be estimated for a purely linear problem which gives estimates beyond the natural NLS time scale. The inverse scattering transform allows us to transfer these estimates to the original variables.</p>