  A comprehensive program of \cp~studies in heavy flavour decays has to go
beyond observing large \cp asymmetries in nonleptonic B decays and finding that
the sum of the three angles of the KM triangle is consistent with
180$^{\circ}$. There are many more correlations between observables encoded in
the KM matrix; those can be expressed through five KM triangles in addition to
the one usually considered. To test the completeness of the KM description one
has to obtain a highly overconstrained data set sensitive to ${\cal O}(\lambda
^2)$ effects with $\lambda = \sin \theta_C$. Those fall into two categories:
(i) Certain large angles agree to leading order only, yet differ in order
$\lambda ^2$ in a characteristic way. (ii) Two observables angles are - for
reasons specific to the KM ansatz - ${\cal O}(\lambda ^2)$ and ${\cal
O}(\lambda ^4)$ thus generating an asymmetry of a few percent and of about 0.1
%, respectively. The former can be measured in $B_s \to \psi \eta, \psi \phi$
{\em without} hadronic uncertainty, the latter in Cabibbo suppressed D decays.
The intervention of New Physics could boost these effects by an order of
magnitude. A special case is provided by $D^+ \to K_{S,L}\pi ^+$ vs. $D^- \to
K_{S,L}\pi ^-$. Finally, \cp~asymmetries involving $D^0 - \bar D^0$
oscillations could reach observable levels only due to New Physics.
