Recently published observational studies of the stable surface layer have produced several quite different prescriptions for the universal functions required by the Monin-Obukhov similarity hypothesis for the fully turbulent surface layer. Three such formulations are described and the different relationships between the surface turbulent fluxes and standard (model) profile variables implied by them are illustrated and compared. The results provide insight to help discriminate between the choices available to the modeller. It is argued that the formulation of Hicks (1976) is that best suited to modelling the surface turbulent fluxes compatible with both our current understanding of the stable boundary layer and the need in a numerical model to estimate fluxes representative over the area of a grid-box or element. A full description of the general procedure for determining surface-layer bulk transfer coefficients from Monin-Obukhov similarity functions is given.