A microwave FM-CW radar can obtain the complete spectrum of radial velocities of both precipitation particles and refractive-index fluctuations in the optically clear air. Heretofore the extraction of the Doppler spectrum from this type of radar was believed to be a formidable, if not impossible, task. We have implemented a Doppler processing technique that uses a data acquisition system developed for pulsed Doppler radar. We present Doppler spectra obtained with a zenith-pointing FM-CW radar that demonstrate this new capability. In addition to the strong refractive-index layers observed by the FM-CW radar in the optically clear air, there is evidence that scattering from a background continuum of Cn2 can be detected when a Doppler operating mode is employed.