We consider the Doppler power spectra calculated from radar precipitation echos. It is shown that receiver noise can produce a spurious linear realtion between the spectral width and radar range. This effect occurs at all elevation angles and disappears when the effects of receiver noise are eliminated by means of a thresholding technique. A simple model explains why this effect occurs when the signal spectrum is sufficiently narrowband and the variation of radar reflectivity isnot too great over the range interval of interest. Examples are given from data taken with a coherent X-band radar.