  We study the bounded from below (BFB) conditions on a class of three Higgs
doublet models (3HDM) constrained by the symmetry groups U(1)xU(1), U(1)xZ2 and
Z2xZ2. These constraints must be implemented on both the neutral (BFB-n) and
charged (BFB-c) directions. The exact necessary and sufficient BFB conditions
are unknown in the Z2xZ2 case. We develop a general strategy using lower bounds
to find sufficient conditions for BFB-n and BFB-c and apply it to these
symmetries. In addition, we investigate the concern that the use of safe
sufficient conditions can ignore valid points which would yield distinct
physical consequences. This is done by performing a full phenomenological
simulation of the U(1)xU(1) and U(1)xZ2 models, where exact necessary and
sufficient BFB conditions are possible. We look specifically at the points
allowed by exact solutions but precluded by safe lower bounds. We found no
evidence of remarkable new effects, partly reassuring the use of the lower
bounds we propose here, for those potentials where no exact necessary and
sufficient BFB conditions are known.
