We propose two-grid iteration methods for Symm's integral equation discretized by quadrature-collocation or quadrature methods. Asymptotically the optimal order of error estimate is achieved already on the fist iteration, for some modifications on the second iteration. This enables us to introduce some solvers which are of the optimal convergence order and cheap in a practical implementation; the cost varies between 0 (N') and O(N1og N ) arithmetic operations. Numerical experiments confirm the approximation properties of the schemes. doesn't equal 1, see [13], [18]. Introduce the standard parametrization zy(t> = e -l J 2 cos 2nt , z i ( t ) = e-'/'sin 2nt of the circle ro of radius e-l/'. One can decompose equation (1.2) into Integral Equations Appl., 1 (1988), 549-579 485-495