  We demonstrate a new type of cancellation of contributions to the electron
and neutron electric dipole moments (EDMs) that occurs in three Higgs doublet
models (3HDMs) when CP violation appears in the charged Higgs sector. The
cancellation becomes exact when the two physical charged Higgs bosons in the
model are degenerate in mass. Depending on the model parameters, degeneracies
at the 10\% level are however sufficient to evade current bounds on the
electron and neutron EDMs. We demonstrate that viable parameter space remains
with both charged Higgs bosons lighter than 500 GeV and large CP-violating
phases while also satisfying theoretical constraints from perturbativity and
experimental ones from $\bar{B} \to X_s \gamma$ and direct searches.
