In Two Higgs Doublet Models shaped by some unbroken symmetry, placing perturbativity requirements on the quartic couplings can imply that the allowed masses of all the fundamental scalars are bounded from above, i.e. there is no decoupling regime for the new scalars. This important property is analysed in detail for the only two viable scenarios, the case with Z 2 symmetry and the case with CP symmetry. It is also noticeable that one exception arises in each case: when the vacuum is assumed to respect the imposed symmetry, a decoupling regime can nevertheless appear without violating perturbativity requirements. In both models with no decoupling regime, soft symmetry breaking terms can however lead to such a decoupling regime: the possibility that this regime might be unnatural, since it requires some fine tuning, is also analysed.