Ship-based measurements of wind speed and direct fluxes are affected by airflow distortion that can lead to a tilt of the wind vector as well as acceleration or deceleration of the wind speed. Direct flux measurements are additionally affected by the fluctuating velocity of the platform. The classic approach is to first correct the wind speed for angular and translational platform velocities and thereafter rotate the wind vector into the mean flow. This study finds that for ships under way, this leads to an overestimation of the vector tilt and biased flux estimates. This may explain the common observation that flux estimates from ships in transit have lower quality than measurements taken on station. Here an alternative approach is presented, where the flow-distortion-induced tilt of the wind vector is estimated from the 3D wind speed measurements and applied to the apparent wind vector. The tilt correction is carried out after correction for the fluctuating part of the platform velocity but before removing the ship's mean translational velocity. This new method significantly improved the agreement of direct momentum flux measurements made from a ship under way with the parameterization of the COARE3.5 bulk model. The sensitivity of the eddy covariance measurements of momentum and scalar fluxes to the choice of the tilt-motion correction method is analyzed, and this study proposes that a reanalysis of previous direct flux measurements with the new method discussed here can improve researchers' understanding of air-sea interaction.