One of the problems in linearized seismic inverse scattering, which has received little attention so far, is the existence of large gaps in the acquisition geometry due to the use of a limited number of sources and receivers. Frequently used Born inversion methods do not take this kind of sampling effect into account. Therefore, especially for three-dimensional problems, the results may suffer from serious artefacts. These problems are partially overcome by using iterative methods, based on the minimization of an error norm. For two-dimensional test problems, the authors have found that iterative methods give significantly more accurate results for sparsely sampled data. For large-scale seismic inverse problems, the rate of convergence of any iterative method is extremely important. The authors have found that fast convergence rates can be achieved with the aid of methods that are preconditioned with the Born inverse scattering operator. In particular, the rate of convergence of the preconditioned successive overrelaxation method and the preconditioned Krylov subspace method have been found to be much faster than the widely used conjugate gradient method. With these new methods, the authors have obtained acceptable results for problems containing as many as 90000 unknowns, after only four iterations.