Presented in this Letter is the IncDFT method, which utilizes the difference density to compute the DFT numerical integration, and is formulated so that the problem of using non-linear functionals is circumvented and proper mathematic consistency is maintained. As convergence is approached, an increasing amount of values associated with the numerical quadrature can be neglected. The IncDFT method has been implemented with a variable threshold in Q-Chem 2.1, and yields up to 45% savings in the time needed for the integration procedure with negligible loss in accuracy. (c) 2005 Elsevier B.V. All rights reserved.