  We describe a model for the scalar sector where all interactions occur either
at an ultra-high scale L_U ~ 10^16 - 10^19 GeV or at an intermediate scale
L_I=10^9 - 10^11 GeV. The interaction of physics on these two scales results in
an SU(2) Higgs condensate at the electroweak (EW) scale, L_EW, through a
seesaw-like Higgs mechanism, L_EW ~ (L_I)^2/L_U, while the breaking of the SM
SU(2)XU(1) gauge symmetry occurs at the intermediate scale L_I. The EW scale
is, therefore, not fundamental but is naturally generated in terms of
ultra-high energy phenomena and so the hierarchy problem is alleviated. We show
that our ``seesaw-Higgs'' model predicts the existence of sub-eV neutrino
masses which are generated through a ``two-step'' seesaw mechanism in terms of
the same two ultra-high scales: m_nu ~ (L_I)^4/(L_U)^3 ~ (L_EW)^2/L_U. We also
show that our seesaw Higgs model can be naturally embedded in theories with
tiny extra dimensions of size R ~ 1/L_U ~ 10^{-16} fm, where the seesaw induced
EW scale arises from a violation of a symmetry at a distant brane if there are
7 tiny extra dimensions.
