A new global model of radial variations in intrinsic shear and compressional attenuation, Qμ(r) and Qκ(r), is presented. The model, called QL6, is derived from recent observations of long-period (150 < T < 300 sec) Rayleigh- and Love-wave attenuation and an extensive set of mode decay observations compiled from the literature. Our preferred model consists of six layers of constant Q, where the parameterization of Qμ(r) follows that of the anelastic component of the preliminary reference earth model (PREM). Relative to the commonly used models of PREM and QM1, lower values of Qμ are required in the upper 200 km of the mantle to explain observations of Love-wave attenuation. The observations require a finite level of compressional attenuation, preferentially located in the upper mantle. An analysis using continuous spline-basis functions supports the layered parameterization—with the recovered model possessing strong gradients in Qμ at the 670-km discontinuity; at the bottom of the asthenosphere; and to a lesser extent, at the base of the lithosphere. However, the continuous model does not have a significant discontinuity in Qμ at the 400-km phase boundary.