Complex geometric optics solutions to a system of d-bar equations appearing in the context of electrical impedance tomography and the scattering theory of the integrable Davey-Stewartson II equations are studied for large values of the spectral parameter k. For potentials q is an element of .(-2) H-s(C) for some s is an element of ]1, 2], it is shown that the solution converges as the geometric series in 1/vertical bar k vertical bar(s-1). For potentials q being the characteristic function of a strictly convex open set with smooth boundary, this still holds with s = 3/2, i.e., with 1/root vertical bar k vertical bar instead of 1/vertical bar k vertical bar(s-1). The leading-order contributions are computed explicitly. Numerical simulations show the applicability of the asymptotic formulae for the example of the characteristic function of the disk.