  We examine a quantum dot with $N_{\rm dot}$ levels which is strongly coupled
to leads for varying number of channels $N$ in the leads. It is shown both
analytically and numerically that for strong couplings between the dot and the
leads, at least $N_{\rm dot}-N$ bound states (akin to subradiant states in
optics) remain on the dot. These bound states exhibit discrete charging and,
for a significant range of charging energies, strong Coulomb blockade behavior
as function of the chemical potential. The physics changes for large charging
energy where the same (superradiant) state is repeatedly charged.
