Observational data in the atmosphere indicate that conventionally defined drag and heat transfer coefficients increase rapidly as wind speed falls. It is shown here that, at sufficiently low wind speeds, the observed heat flux is nearly independent of wind speed but the drag increases linearly with it. These findings are not consistent with the free-convection limit of the Businger relations for Monin–Obukhov theory, and lend support to the ideas of Ingersoll (1966) and Grachev (1990), till now checked only against laboratory experiments. We propose here that it is useful to define, within the regime of mixed convection, a sub-regime of ‘weakly forced convection’ in which, to a first approximation, the heat flux is determined by temperature differentials as in free convection and the momentum flux by a perturbation, linear in wind, on free convection. It is further proposed that this regime is governed by velocity scales determined by the heat flux (rather than by the friction velocity as in classical turbulent boundary layer theory). Three candidates for the heat-flux velocity scale are considered; novel definitions of the drag and heat exchange coefficients, based on the preferred scale, are found to show very weak dependence on wind speed up to values of about 5–10 m s$^{-1}$; but there is some evidence that the usefulness of heat-flux scaling may extend beyond the velocity limits where pure free-convection scaling for heat flux is valid.