The inertial-dissipation method has long been used to estimate air-sea fluxes from ships because it does not require correction for ship motion. A detailed comparison of the inertial-dissipation fluxes with the direct covariance method is given, using data from the Humidity Exchange Over the Sea (HEXOS) main experiment, HEXMAX. In this experiment, inertial-dissipation packages were deployed at the end of a 17 m boom, in a region relatively free of flow distortion; and on a mast 7 m above the platform (26 m above the sea surface) in a region of considerable flow distortion. An error analysis of the inertial-dissipation method indicates that stress is most accurately measured in near-neutral conditions, whereas scalar fluxes are most accurately measured in near-neutral and unstable conditions. It is also shown that the inertial-dissipation stress estimates are much less affected by the flow distortion caused by the platform as well as by the boom itself. The inertial-dissipation (boom and mast) and boom covariance estimates of stress agree within ±20%. The latent heat flux estimates agree within approximately ±45%. The sensible heat flux estimates agree within ±26% after correction for velocity contamination of the sonic temperature spectra. The larger uncertainty in the latent heat fluxes is due to poor performance of our Lyman-α hygrometers in the sea spray environment. Improved parameterizations for the stability dependence of the dimensionless humidity and temperature structure functions are given. These functions are used to find a best fit for effective Kolmogorov constants of 0.55 for velocity (assuming a balance of production and dissipation of turbulent kinetic energy) and 0.79 for temperature and humidity. A Kolmogorov constant of 0.51 implies a production-dissipation imbalance of approximately 12% in unstable conditions.