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.