  We consider models with any number of Higgs doublets and study the conditions
for decoupling. We show that, under very general circumstances, all the
quadratic coefficients of the scalar potential must be present, except in
special cases, which include terms related to directions of vanishing vacuum
expectation values. We give a few examples. Moreover, we show that the
decoupling of all charged scalars implies the decoupling of all extra neutral
scalars and vanishing $\mathcal{CP}$ violation in scalar-pseudoscalar mixing.
