Fundamental-mode Rayleigh wave attenuation data for eastern North America can be explained by a frequency-independent model of shear wave internal friction (Qβ-1) as well as by numerous frequency-dependent models of the crust. Assuming that Qβ-1 (ω, z) =C(z)ω-&zgr;, fundamental-mode Rayleigh wave data were inverted to obtain several frequency-dependent Qβ-1 models corresponding to different distributions of &zgr;. Limiting values of &zgr; were then sought by computing attenuation coefficients for the higher Rayleigh modes for the various models. The calculated attenuation coefficients were compared to reported values for Lg and the first higher Rayleigh mode as observed at periods between 1 and 10 s in eastern North America. If it is assumed that &zgr; is constant over the entire period range between 1 and 40 s, then its most likely value lies between 0.3 and 0.5. The frequency-independent case (&zgr;=0.0) can definitely be rejected. Better fits to the data can be achieved by allowing &zgr; to very with period, increasing relatively rapidly with decreasing period at periods of 4 and less. It is possible that a peak in Qβ-1 occurs at periods between 1 and 4 s. Additional higher-mode data will be needed in that range, however, before the existence of such a peak can be verified or rejected. All Qβ-1 models resulting from the inversion process include a low-Q zone with a base at midcrustal depths. The low-Q zone is, however, marginally resolvable for only some of the frequency-dependent models of this study.