We analyze approximately four years of heat-flux measurements at two levels, profiles of air temperature, and multiple measurements of the water temperature collected at a coastal zone site. Our analysis considers underestimation of the sea-surface flux due to vertical divergence of the heat flux between the surface and the lowest flux level. We examine simple relationships of the heat flux to the wind speed and stratification and the potential influence of fetch and temperature advection. The fetch ranges from about 4 km to near 400 km. For a given wind-direction sector, the transfer coefficient varies only slowly with increasing instability, but decreases significantly with increasing stability. The intention here is not to recommend a new parameterization but rather to establish relationships that underly the bulk formula that could lead to assessments of uncertainty and improvement of the bulk formula.