We investigate periodicities in redshift samples corrected for the apparent motion of the solar system relative to the cosmic background radiation. The samples used for the initial study of CBR-related periodicities are composed of data on galaxies with 21 cm profiles of intermediate width taken by Tifft and Tifft and Cocke at the 300-ft telescope at Green Bank. Referred to a coordinate system at rest with respect to the CBR, these data are found to be periodic near the 72 km s-1 period previously associated with redshift quantization. Spectral power methods are used to evaluate the high significance levels found for the association. The significance is verified by searching for periodicities in a large volume of velocity space. The search shows that random occurrences at the specified period occur at a level consistent with the fact that the coincidence with the CBR rest frame is very improbable. It is further shown that a phase shift occurs in the periodicity near 21 cm profile widths of 250 km s-1. Other data confirm the correspondence with the CBR rest frame and the effects of dependence on profile width; namely, 21 cm data by Fisher and Tully and data by Giovanelli and Haynes for the Perseus supercluster. The Fisher-Tully data for moderate to large profile widths confirm the presence of significant periodicities close to 72 km s-1 both below and above profile widths near 250 km s-1 where the phase shift occurs. The Giovanelli and Haynes data extend the analysis to galaxies with very wide 21 cm profiles and confirm the presence of a previously known period near one half of 72 km s-1 as well as the CBR association.