The estimates of the sensible and latent heat fluxes are explored for two semi-arid locations using standard measurements of temperature and humidity at two levels in the surface layer. The sensible heat flux estimated with the stability functions proposed by Businger has values within the tolerable error in complex terrain, except when the surface is wet and irradiation is high. These cases correspond to a regime dominated by evaporation, typically with Bowen ratios below one, that needs modified stability functions. For the latent heat flux, the Businger function is applicable only over dry soils with a sensible heat flux similar to or slightly larger than the latent heat flux. Instead, new functions are necessary when sensible heat clearly dominates, or when the underlying surface contains enough humidity. In addition, the turbulent Lewis number -defined as the ratio between the turbulent diffusion coefficients for heat and moisture- increases with the Bowen ratio, getting values larger than one for Bowen ratios above 2.5. These results suggest that mixing efficiencies for heat and matter are different except for a narrow range of conditions. Flux-gradient deviations for humidity correspond to cases with dissimilarity between temperature and water vapour caused by surface heterogeneity, affecting the relative transport efficiency between heat and moisture. Instead, the deviations for temperature observed over moderately wet surfaces does not imply a breakdown in the temperature-humidity correlation.