To improve the quality of scalar-flux measurements, the two-point covariance between the vertical velocity w̃ and a scalar s̃, separated in space both horizontally and vertically, is studied. The measurements of such two-point covariances between vertical velocity and temperature with horizontal and vertical separations show good agreement with a symmetric turbulence model when the displacement is horizontal. However, a similar model does not work for vertical displacements because up–down asymmetry exists; that is, there is a lack of reflection symmetry of the covariance function. The second-order equation for conservation of two-point covariance of w̃ and s̃ reveals the reason for this up–down asymmetry and determines its character. On the basis of our measurements, the “loss of flux” for a given lateral displacement decreases with increasing height of the sensors. For example, at a height of z = 10 m with a sensor displacement of D = 0.2 m, less than 1% of the flux is lost, whereas at z = 1 m the same instrument configuration gives rise to a loss of 13%. Also, when the displacement is vertical, the “flux loss” decreases with height if the displacement is kept constant, but in this case the asymmetry causes the loss to be much smaller if the scalar sensor is positioned below the anemometer: if the mean height is 1 m and the displacement 0.2 m, the loss is 18% with the scalar sensor over the anemometer and only 2% if the instrument positions are interchanged. The authors conclude that when measuring close to the ground, the separation should be vertical with the scalar sensor below the anemometer. In this way a symmetric (omnidirectional) configuration with a minimum of flux loss is obtained.