Fitting of the lunar laser ranging (LLR) data to the quality-factor power scaling law Q ∼ χ p rendered a small negative value of the exponential: p = −0.19 (Williams et al., 2001). Further attempts by the JPL team to reprocess the data led to p = −0.07. According to Williams and Boggs (2009), "Q for rock is expected to have a weak dependence on tidal period, but it is expected to decrease with period rather than increase."The most recent estimates of the tidal contribution to the lunar physical librations (Williams & Boggs, 2015) still predict a mild increase of Q with period: from Q = 38 ± 4 at one month to Q = 41 ± 9 at one year, yielding p = −0.03 ± 0.09. Efroimsky (2012aEfroimsky ( , 2012b suggested that since the frequency-dependence of k 2 /Q always has a kink shape, like in Figure 1, the negative slope found by the LLR measurements could be consistent with the peak of the kink residing between the monthly and annual frequencies. This interpretation entails, for a homogeneous Maxwell or Andrade lunar model, very low values of the mean viscosity, indicating the presence of partial melt.Our goal now is to devise an interpretation based on the Sundberg-Cooper model. Within that model, the kink contains not one but two peaks, and we are considering the possibility that the negative slope of our interest is due to the monthly and annual frequencies bracketing either this peak or the local inter-peak minimum.