  The Two-Higgs Doublet Model (2HDM) is one of the most popular and natural
extensions of the Higgs sector; but it has two potential fine-tuning problems,
related to the electroweak (EW) breaking and the requirement of alignment with
the SM Higgs boson. We have quantified the fine-tunings obtaining analytical
expressions, both in terms of the initial 2HDM parameters and the physical ones
(masses, mixing angles, etc.). We also provide simple approximate expressions.
We have taken into account that the fine-tunings are not independent and
removed the "double counting" by projecting the variations of the alignment
onto the constant-${\rm v}^2$ hypersurface. The EW and the alignment
fine-tunings become severe in different, even opposite, regions of the
parameter space, namely in the regimes of large and small extra-Higgs masses,
respectively; emerging an intermediate region, $500\ {\rm GeV} \leq \{m_H, m_A,
m_{H^\pm}\} \leq 700\ {\rm GeV}$, where both are acceptably small. We also
discuss a remarkable trend that is not obvious at first glance. Namely, for
large $\tan\beta$ both the EW and the alignment fine-tunings become mitigated.
In consequence, the 2HDM becomes quite natural for $\tan\beta\geq {\cal O}
(10)$, even if $m_H, m_A, m_{H^\pm}$ are as large as 1500 GeV. We explain why
this is not the case for the 2HDM stemming from supersymmetry. We have
illustrated all these trends by numerically analyzing several representative
scenarios.
