  There has been a great interest in three Higgs doublet models (3HDM)
symmetric under an exact A4 symmetry. We provide the complete analytic
necessary and sufficient conditions for a point to be the global minimum along
the neutral directions in such models, discussing many of the subtleties
involved. We also present a number of numerical examples, to highlight those
issues. We then turn to the directions which break electric charge, presenting
a safe analytical sufficient condition for bounded from below (BFB) potentials.
Based on extensive numerical simulations, we discuss one conjecture on BFB
along charge breaking directions.
