Iterative diagonalization of the Hamiltonian matrix is required to solve very large electronic-structure problems. Present algorithms are limited in their convergence rates at low wave numbers by stability problems associated with large changes in the Hartree potential, and at high wave numbers with large changes in the kinetic energy. A new method is described which includes the effect of density changes on the potentials and properly scales the changes in kinetic energy. The use of this method has increased the rate of convergence by over an order of magnitude for large problems.