The discrete ordinates method is widely used to solve the radiative transfer equation, often yielding satisfactory results. However, in the presence of strongly forward scattering media, this method does not generally conserve the scattering energy and the phase function asymmetry factor. Because of this, the phase function should be normalized so that the scattering energy and the asymmetry factor are conserved. Various authors have proposed different normalization techniques. Three of these are compared in the present work, along with two other methods, one based on the finite volume method (FVM) and another one based on the spherical harmonics discrete ordinates method (SHDOM). In this study, these techniques are applied to three benchmark test cases, namely a three-dimensional cubic domain with a purely scattering medium, an axisymmetric cylindrical enclosure containing an emitting-absorbing-scattering medium, and a three-dimensional transient problem with collimated radiation. The present results confirm previous findings concerning the need to normalize the phase function in such a way that both the scattered energy and the phase function asymmetry factor are conserved. Whenever the normalization guarantees that, the predictions are satisfactory. This may be difficult to achieve when the FVM is used and the asymmetry factor is close to unity. The accuracy of the SHDOM seems also to decrease when that factor is close to one, even though the influence of the various optical parameters on the results needs to be further investigated.