We study the conformal wave equation square_g ψ+ 2/l² ψ= 0 on 4-dimensional Schwarzschild–Anti de Sitter spacetimes under dissipative boundary conditions. We prove boundedness and decay of the non-degenerate energy of ψ at an arbitrary polynomial rate of (1+v)⁻ⁿ provided that we control the (up to) n-times T-commuted energy. This contrasts with the inverse logarithmic decay obtained under Dirichlet boundary conditions and is in line with the result obtained in the pure Anti-de Sitter case under dissipative boundary conditions. In particular, the decay is not affected by the additional trapping at the photon sphere.