  A large hierarchy between the electroweak scale and virtually any new scale
of beyond-Standard-Model physics is often claimed to be unnatural. Sometimes,
the apparent disparity between the measured Higgs mass and the size of the
typical loop corrections encountered within such schemes is even interpretted
as a profound indication that one should expect a remedy just behind the
corner, probably in form of a new physics such as low-scale supersymmetry, new
strong dynamics etc. In reality, all such potentially large corrections in the
one- and two-point Green's functions cancel with each other in the physical
Higgs mass $m_{H}$ which eventually turns out to be driven only by the
electroweak VEV $v$. This, naively, may look like a miracle, the more that the
standard perturbative approach often makes it irresistible to discuss the
magnitudes of those corrections as if, individually, they were physically
relevant. To shed some more light on this conundrum we advocate a method based
on the symmetry properties of the Coleman-Weinberg effective potential which
not only makes it very clear why $m_H\propto v$ to all orders in the
perturbative expansion but, at the same time, it does not require any
inspection of the explicit form of the tadpole equations whatsoever. Besides
simplifying the calculations considerably it makes the "internal composition"
of the VEV in terms of the high-scale parameters essentially irrelevant. We
exemplify these findings on an extended series of specific simplified models in
which the role of the heavy dynamics is played by all "reasonable" types of
fields (barring gravity), i.e., by a heavy scalar, a heavy (Majorana) fermion
and a heavy vector, respectively. We show that the dependence of $m_{H}$ on the
heavy scale follows the expectation based on dynamical arguments such as the
decoupling theorem.
