The size of the interaction region grid in a discrete Kohn variational reactive scattering calculation may be minimized by using distorted waves (DWs) in the trial wave function. Fully converged state-to-state results may be obtained with a small grid if (1) closed channels are included in the coupled channels expansion of the DWs and (2) asymptotically vanishing DWs are included in the trial wave function. This may be done without spoiling the sparsity of the interaction region Hamiltonian, which allows the use of an iterative method for solving the linear equations. We define boundary conditions for the regular, irregular, and asymptotically closed DWs, that minimize the number of DWs needed for convergence. The application to the reaction H+O2-->OH+O, is given in part II.