The capability to measure Q factors at cryogenic temperatures enhances the ability to study relaxation processes in solids. Here we present a high-precision cryogenic setup with the ability to measure Q factors of at least 10(9). This level of sensitivity offers new potential for analyzing relaxation processes in solids and for correlating mode shape and relaxation strength. Our improved method of mechanical spectroscopy, cryogenic resonant acoustic spectroscopy of bulk materials, is verified by identifying relaxation processes in low-loss quartz crystals. For the first time, we observe additional damping peaks. The mechanical Q factors of different modes of cylindrical crystalline quartz substrates were measured from 300 down to 6 K. Resonant modes with frequencies between 10 and 325 kHz were excited without contact to the substrates and the ring down of the amplitudes was recorded using an interferometric vibration readout.