  Two-Higgs-Doublet-Models (THDMs) are among the simplest extensions of the
standard model and are intensively studied in the literature. Using on-shell
parameters such as the masses of the additional scalars as input, corresponds
often to large quartic couplings in the underlying Lagrangian. Therefore, it is
important to check if these couplings are for instance in agreement with
perturbative unitarity. The common approach for doing this check is to consider
the two-particle scattering matrix of scalars in the large centre-of-mass
energy limit where only point interactions contribute. We show that this is not
always a valid approximation: the full calculation including all tree-level
contributions at finite energy can lead to much more stringent constraints. We
show how the allowed regions in the parameter space are affected. In
particular, the light Higgs window with a second Higgs below 125 GeV completely
closes for large values of the $Z_2$ breaking parameter $|M_{12}|$. We also
compare against the loop corrected constraints, which use also the large
$\sqrt{s}$ approximation, and find that (effective) cubic couplings are often
more important than radiative corrections.
