Linear model theory is used to find exact confidence intervals for wind components from radial wind speeds observed using a VHF Doppler radar. The theory is also used to evaluate exact confidence intervals for wind direction. However, exact confidence intervals for wind speeds can only be found where the errors in the two estimated horizontal wind speed components are equal. Thus, in the general case, a Taylor expansion has to be used to give approximate confidence intervals for wind speeds. It is shown that irrespective of the wind vector, the mean confidence interval for the wind components, or the confidence volume of the wind vector, can be minimized by using radar beams with the largest off-vertical angles. However, there is no optimal sounding strategy for the measurement of wind speed or direction that can be defined before making any measurements.