  We investigate the possibility of observing direct CP violation in
self-tagging B-meson decays of the type b -> d J/\psi. The CP asymmetry can be
generated due to strong or electromagnetic scattering in the final state, or
due to long distance effects. The first two contributions give asymmetries of a
few 10^(-3), in the standard model. The long distance effects are hard to
estimate, but it cannot be excluded that they yield asymmetries of about 1%.
