We propose a new preconditioner for computing the self-consistent problem in Kohn-Sham density functional theory, based on the local density of states. This preconditioner is inexpensive and able to cure the long-range charge sloshing known to hamper convergence in large, inhomogeneous systems such as clusters and surfaces. It is based on a parameter-free and physically motivated approximation to the independent-particle susceptibility operator, appropriate for both metals and insulators. It can be extended to semiconductors by using the macroscopic electronic dielectric constant as a parameter in the model. We test our preconditioner successfully on inhomogeneous systems containing metals, insulators, semiconductors and vacuum.