Penguin pollution in $\beta$ and $\beta_s$

The mixing-induced CP asymmetries in $B_d \to J/\psi K_S$ and $B_s \to J/\psi \phi$ are essential to detect or constrain new physics in the $B_d\! - \overline{\!B}{}_d$ and $B_s\! - \overline{\!B}{}_s$ mixing amplitudes, respectively. To this end one must control the penguin contributions to the decay amplitudes, which affect the extraction of fundamental CP phases from the measured CP asymmetries. Although the "penguin pollution" is doubly Cabibbo-suppressed, it could compete in size with current experimental errors. In this talk I present a calculation of the penguin contributions treating QCD effects with soft-collinear factorisation and compare method and results with the alternative approach employing flavour-SU(3) symmetry. As a novel feature, I present results for the penguin pollution in $b\to c\overline c d$ modes.