This paper reports on the improvements of flux enforcement and auxiliary state farfield boundary conditions for Euler and Navier–Stokes computational fluid dynamics (CFD) codes. The new conditions are based on 1D characteristic data and also on the introduction in the boundary conditions of certain numerical features of the numerical scheme used for the interior of the domain. In the presence of strong streamwise gradients of the flow field at the farfield boundaries, the new conditions perform significantly better than their conventional counterparts in that they (a) preserve the order of the space discretization and (b) greatly reduce the error in estimating integral output. A coarse-grid CFD analysis of the compressible flow field in an annular duct for which an analytical solution is available yields a mass flow error of 62% or 2%, depending on whether the best or the worst farfield boundary condition (BC) implementation is used. The presented BC enhancements can be applied to structured, unstructured, cell-centered, and cell-vertex solvers.