A simple method for computing the full spectrum of the linear (nonadiabatic) radial modes is implemented and tested on RR Lyrae models. The growthrates of the vibrational modes display unexpected, but physically correct undulations as a function of period, with the 8th through 10th overtones almost unstable. Caution must be exercised when only a small number of meshpoints is used, or when the meshpoints are not well distributed, as some of these overtones may become unstable, clearly an artifact of the differencing. The role that such unstable high overtones can play in hydrodynamic calculations is demonstrated.