The discrete ordinates method (DOM) and discrete transfer method (DTM) were evaluated from the viewpoints of both predictive accuracy and computational economy by comparing their predictions with exact solutions available from a box-shaped enclosure problem with steep temperature gradients. Comparative testing shows that the S-4 approximation produces better accuracy in radiative energy source term than in flux density in three orders of magnitude less CPU time than that required by the DTM. The S-4 approximation can therefore be recommended to be used in conjunction with CFD codes.