We propose a new method that enables Q-compensation after depth imaging and within the framework of depth domain inversion. The approach relies on deterministic operators that capture the dip-dependent amplitude and phase anelastic effects seen by the waves as they propagate through a 3D anelastic medium, and corrects for them by inversion in the image domain. It provides fully deconvolved images (reflectivity) compensated for both anelastic and illumination effects. We demonstrate this approach in the context of reverse time migration (RTM) and show its potential with a complex synthetic.