  We propose the use of basis invariants, valid for any choice of CP
transformation, as a powerful approach to studying specific models of CP
violation in the presence of discrete family symmetries. We illustrate the
virtues of this approach for examples based on $A_4$ and $\Delta(27)$ family
symmetries. For $A_4$, we show how to elegantly obtain several known results in
the literature. In $\Delta(27)$ we use the invariant approach to identify how
explicit (rather than spontaneous) CP violation arises, which is geometrical in
nature, i.e. persisting for arbitrary couplings in the Lagrangian.
