  We perform an exhaustive analysis of the most general Higgs sector of the
minimal left-right symmetric model (MLRM). We find that the CP properties of
the vacuum state are connected to the Higgs spectrum: if CP is broken
spontaneously, the MLRM does not approach the Standard Model in the limit of a
decoupling left-right symmetry breaking scale. Depending on the size of the CP
phases scenarios with extra non-decoupling flavor-violating doublet Higgses or
very light SU(2) triplet Higgses emerge, both of which are ruled out by
phenomenology. For zero CP phases the non-standard Higgses decouple only if a
very unnatural fine-tuning condition is fulfilled. We also discuss
generalizations to a non-minimal Higgs sector.
