  Models with three Higgs doublets (3HDM) are the source of much recent
activity, for they are key components of many solutions to the problems of the
Standard Model; from extra sources of CP violation to Dark Matter candidates.
We compute explicitly the theoretical bounds for all symmetry-constrained 3HDM
arising from the perturbative unitarity of two-to-two scattering amplitudes. In
addition, we propose a method based on principal minors that foregoes
diagonalization and which is preferable in all models (not only 3HDM) dealing
with large scattering matrices.
