Frequency-modulated laser transient absorption has been used to monitor the ground-state rotational energy-transfer rates of CN radicals in a double-resonance, depletion recovery experiment. When a pulsed laser is used to burn a hole in the equilibrium ground-state population of one rotational state without velocity selection, the population recovery rate is found to depend strongly on the Doppler detuning of a narrow-band probe laser. Similar effects should be apparent for any relaxation rate process that competes effectively with velocity randomization. Alternative methods of extracting thermal rate constants in the presence of these non-thermal conditions are evaluated. Total recovery rate constants, analogous to total removal rate constants in an experiment preparing a single initial rotational level, are in good agreement with quantum scattering calculations, but are slower than previously reported experiments and show qualitatively different rotational state dependence between Ar and He collision partners. Quasi-classical trajectory studies confirm that the differing rotational state dependence is primarily a kinematic effect.