We consider the small-signal response of a rate-equation laser to modulation of the laser cavity length. To avoid nonlinear resonances in modulators and power supplies, we demonstrate that one can hold the modulation frequency and amplitude fixed while varying the cavity detuning to change the resonant response of the laser to modulation, and thereby one can extract the relaxation oscillation frequency and the damping rate of those oscillations. This technique permits a careful study of the relaxation parameters of the laser that govern small oscillations and thereby permits discrimination among several different models recently proposed to describe CO2 laser dynamics. We demonstrate this method of analysis by applying it to such a laser experimentally with the result that the simple rate-equation model is shown to fail while the more complex vibro-rotational model satisfactorily describes the results.