One signature of expulsion of coronal mass ejections (CMEs) from the solar corona is the appearance of transient intensity dimmings in coronal images. These dimmings have generally been assumed to be due to discharge of CME material from the corona, and thus the "dimming regions" are thought of as an important signature of the sources of CMEs. We present spectral observations of two dimming regions at the time of expulsion of CMEs, using the Coronal Diagnostic Spectrometer (CDS) on the SOHO satellite. One of the dimming regions is at the solar limb and associated with a CME traveling in the plane of the sky, while the other region is on the solar disk and associated with an Earth-directed "halo" CME. From the limb event, we see Doppler signatures of approximately equal to 30 kilometers per second in coronal (Fe XVI and Mg Ix) emission lines, where the enhanced velocities coincide with the locations of coronal dimming. This provides direct evidence that the dimmings are associated with outflowing material. We also see larger (approximately equal to 100 kilometers per second). Doppler velocities in transition region (0 v and He I) emission lines, which are likely to be associated with motions of a prominence and loops at transition region temperatures. An "EIT wave" accompanies the disk event, and a dimming region behind the wave shows strong blue-shifted Doppler signatures of approximately equal to 100 kilometers per second in 0 v, suggesting that material from the dimming regions behind the wave may be feeding the CME.