Using reference source time functions, broadband velocity waveforms of PKIKP in the distance range 150--180¿ are inverted for a viscoelastic model of inner core attenuation. A mean Qα at 1 Hz of 307 ¿ 90 is determined from 345 available PKIKP ray paths. Both global and regional results find a depth-dependent attenuation in the deep inner core, with anisotropic attenuation resolved in regional results. Attenuation is much stronger in the upper 300 km of the inner core. The preferred model of viscoelastic attenuation is frequency dependent, with very weak velocity dispersion. Our data do not resolve any hemispherical differences of attenuation in the deep inner core.