Recently observed anomalies in the Bs → J/ψφ decay and the like-sign dimuon asymmetry A b sl hint at possible new physics (NP) in the Bs − Bs mixing. We parameterize the NP with four modelindependent quantities: the magnitudes and phases of the dispersive part M12 and the absorptive part Γ12 of the NP contribution to the effective Hamiltonian. We constrain these parameters using the four observables ∆Ms, ∆Γs, the mixing phase β J/ψφ s , and A b sl . Our quantitative fit indicates that the NP should contribute a significant dispersive as well as absorptive part. In fact, models that do not contribute a new absorptive part are disfavored at more than 99% confidence level. We extend this formalism to include CPT violation, and show that CPT violation by itself, or even in presence of CPT-conserving new physics without an absorptive part, helps only marginally in the simultaneous resolution of these anomalies. The NP absorptive contribution to Bs − Bs mixing therefore seems to be essential, and would imply a large branching fraction for channels like Bs → τ + τ − .