An alternative method for obtaining high and interior eigenvalues of a dense spectrum is presented. The method takes advantage of the accurate, well-tested and fully understood algorithms for the fast Fourier transform to create, in a natural manner, a 'window' containing only a small number of eigenvalues of the spectrum. The method is easy to implement, stable, efficient and accurate. (C) 1999 Elsevier Science B.V. All rights reserved.