A scheme was formulated by Firmin that iterates between successive approximations to the boundary-layer flow, the aerofoil pressure distribution (calculated in inviscid flow for the aerofoil-plus-displacement surface) and their mutual interaction. In the method, inviscid theory is restricted to first order but incorporates terms that account for the effects of wake curvature. The accuracy of this method was assessed by comparison with experimental data, the effects of tunnel constraint being taken into account in an extension of the method. The method is outlined and comparisons made with fully-corrected experimental data for one particular aerofoil. Comments on some of the limitations of the method are included.