Results are presented for an efficient solution method for second-order accurate discretizations of the 2D steady Euler equations. The solution method is based on iterative defect correction. Several schemes are considered for the computation of the second-order defect. In each defect correction cycle, the solution is computed by non-linear multigrid iteration, in which collective symmetric Gauss-Seidel relaxation is used as the smoothing procedure. A finite volume Osher discretization is applied throughout. The computational method does not require any tuning of parameters. The airfoil flow solutions obtained show a good resolution of all flow phenomena and are obtained at low computational costs. The rate of convergence is grid-independent. The method contributes to the state of the art in efficiently computing flows with discontinuities.