The transfer coefficients for momentum and heat have been determined for 10 m neutral wind speeds (U10n) between 0 and 12 m/s using data from the Surface of the Ocean, Fluxes and Interactions with the Atmosphere (SOFIA) and Structure des Echanges Mer-Atmosphere, Proprietes des Heterogeneites Oceaniques: Recherche Experimentale (SEMAPHORE) experiments. The inertial dissipation method was applied to wind and pseudo virtual temperature spectra from a sonic anemometer, mounted on a platform (ship) which was moving through the turbulence field. Under unstable conditions the assumptions concerning the turbulent kinetic energy (TKE) budget appeared incorrect. Using a bulk estimate for the stability parameter, Z/L (where Z is the height and L is the Obukhov length), this resulted in anomalously low drag coefficients compared to neutral conditions. Determining Z/L iteratively, a low rate of convergence was achieved. It was concluded that the divergence of the turbulent transport of TKE was not negligible under unstable conditions. By minimizing the dependence of the calculated neutral drag coefficient on stability, this term was estimated at about −0.65Z/L. The resulting turbulent fluxes were then in close agreement with other studies at moderate wind speed. The drag and exchange coefficients for low wind speeds were found to be Cen × 103 = 2.79U10n−1 + 0.66 (U10n < 5.2 m/s), Cen × 103 = Chn × 103 = 1.2 (U10n ≥ 5.2 m/s), and Cdn × 103 = 11.710n−2 + 0.668 (U10n < 5.5 m/s), which imply a rapid increase of the coefficient values as the wind decreased within the smooth flow regime. The frozen turbulence hypothesis and the assumptions of isotropy and an inertial subrange were found to remain valid at these low wind speeds for these shipboard measurements. Incorporation of a free convection parameterization had little effect.