We apply and compare three model-based Q-compensation approaches. The first two approaches rely upon ray-based attenuated traveltime (t*) modeling operators. One is applied prior to migration, the other one is embedded into a Kirchhoff depth migration algorithm (KDM). The third approach is based on wavepath-consistent t* modeling and is embedded into reverse time migration (RTM). Benefits and drawbacks of each of these methods are discussed and illustrated on a visco-acoustic version of the complex BP 2004 model. While ray-based Q-compensation performs well, especially when embedded within KDM, wavepathconsistent Q-compensation within RTM compensates more complex events and seems worthwhile in highly complex media. However, all approaches are prone to noise amplification issues which must be accounted for.