An empirical strategy for improving modeling of the energy dissipation rate e ij and the velocity-pressure gradient Π ij terms in the transport equations for the Reynolds stresses is proposed on the basis of available direct numerical simulations of the turbulent boundary layer and fully developed turbulent channel flow. The dissipation-rate model takes into account the anisotropy of the dissipation rate not only near the wall but elsewhere in the flow as well. When modeling the velocity-pressure gradient term, the usual split between pressure-transport and redistributive terms is avoided. One consequence of this strategy is the elimination of wall reflection or near-wall correction terms. Wall-topography parameters, such as the distance to the wall and wall-normal vectors, are also absent. Calculations of a turbulent boundary layer over a smooth wall confirm the potential improvements that can be achieved with this approach.