We derive a sum rule which shows how to extend limits from LEP data on
the masses of the lightest CP-even and CP-odd Higgs bosons of a CP-co
nserving two-Higgs doublet model to any two Higgs bosons of a general
CP-violating two-Higgs-doublet model. We generalize the analysis to a
Higgs sector consisting of an arbitrary number of Higgs doublets and s
inglets, giving explicit limits for the CP-conserving and CP-violating
two-doublet plus one-singlet Higgs sectors.