Convergence of the PCG solver of the CMB map-making problem for two different scanning strategy. Different types of lines correspond to different versions of the Toeplitz matrix used in the simulation, as described by the parameter f_knee. Different colours correspond to the two different types of preconditioners: red for the standard block preconditioner M_BD and green for the two-level preconditioner M_2lvl,D whose coarse space Z_D, is made of approximated eigenvectors corresponding to small eigenvalues λ_i of M_BDA. dim(Z) denotes the number of columns in the deflation subspace operator Z_D which is the number of eigenvalues with (Re | λ_i | <ϵ_tol = 0.3).