Granada (Southern Spain) is a place of rare and enigmatic very deep focus earthquakes, the last one on April 11, 2010, with magnitude of 6.3 and depth of 620 km. We use regional broadband recordings to estimate QP and QSin the mantle for frequencies between 0.25 and 8 Hz, computing the spectra of the direct P- and S-waves with their early P- and S coda. We use the spectral decay method, constraining crustalQ to values given in the literature. We obtain robust estimates of QP in 6 frequency bands (0.25, 0.5,1, 2, 4 and 8 Hz) and of QS in 4 bands (0.25, 0.5,1, 2 Hz). QP in the mantle ranges from 13 at 0.25 Hz to 346 at 8 Hz and QS from 59 at 0.25 to 183 at 2 Hz. The frequency dependence is well fitted by Q = Q0fα with α equal to 0.6 for QS and 1.0 for QP, and Q0 equal to 109 for QS and 63 for QP. The QP/QS ratio is less than 1. These are extreme values within the ranges of mantle Q, QP/QS and αvalues reported in the literature, indicating strong scattering attenuation and absence of melt. We propose that such values, rather than being an exception, may approximate the average upper mantle, with solid olivine composition and small-scale heterogeneity.