The stability of basic states consisting of a jet similar to the stratospheric polar night jet and a traveling wave with a single zonal wave number is examined in a linearized nondivergent barotropic model on a sphere. Basic state wave are chosen to resemble observed traveling and stationary features in the winter stratosphere. Results are presented for disturbance growth rates, propagation characteristics, and energy conversion as a function of the basic state wave amplitude. The effects of small amplitude basic state waves on unstable disturbances arising from a zonally symmetric jet are discussed; results are shown where a small amplitude basic state wave dramatically affects the stability characteristics. Evidence is shown that the presence of a traveling wave may favor the appearance of disturbances that include other zonal wavenumbers which move with the basic state wave; this result is discussed in relation to the origin of observed quasi-nondispersive features in the polar winter stratosphere. Results for a stationary wavenumber 1 basic state wave suggest that a distorted polar vortex may be unstable to disturbances that would lead to further distortion. An unstable disturbance for a basic state with an eastward moving wavenumber 2 has components which resemble, in period and location, traveling waves that are observed in the winter stratosphere.