Measurements of CP violation in B d 0  →  J / ψK S 0 and B s 0  →  J / ψϕ decays play key roles in testing the quark-flavour sector of the Standard Model. The theoretical interpretation of the corresponding observables is limited by uncertainties from doubly Cabibbo-suppressed penguin topologies. With continuously increasing experimental precision, it is mandatory to get a handle on these contributions, which cannot be calculated reliably in QCD. In the case of the measurement of sin 2 β from B d 0  →  J / ψK S 0 , the U -spin-related decay B s 0  →  J / ψK S 0 offers a tool to control the penguin effects. As the required measurements are not yet available, we use data for decays with similar dynamics and the SU(3) flavour symmetry to constrain the size of the expected penguin corrections. We predict the CP asymmetries of B s 0  →  J / ψK S 0 and present a scenario to fully exploit the physics potential of this decay, emphasising also the determination of hadronic parameters and their comparison with theory. In the case of the benchmark mode B s 0  →  J / ψϕ used to determine the B s 0 − B ¯ s 0 $$ {B}_s^0-{\overline{B}}_s^0 $$ mixing phase ϕ s the penguin effects can be controlled through B d 0  →  J / ψρ 0 and B s 0 → J / ψ K ¯ * 0 $$ {B}_s^0\to J/\psi {\overline{K}}^{*0} $$ decays. The LHCb collaboration has recently presented pioneering results on this topic. We analyse their implications and present a roadmap for controlling the penguin effects.