A simple method for computing accurate density-dependent dispersion coefficients is presented. The dispersion coefficients are modeled by a generalized gradient-type approximation to Becke and Johnson's exchange hole dipole moment formalism. Our most cost-effective variant, based on a disjoint description of atoms in a molecule, gives mean absolute errors in the C-6 coefficients for 90 complexes below 10%. The inclusion of the missing long-range van der Waals interactions in density functionals using the derived coefficients in a pair wise correction leads to highly accurate typical noncovalent interaction energies. (C) 2011 American Institute of Physics. [doi:10.1063/1.3545985]