  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 the class of such ``seesaw Higgs'' models predict 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. The
neutrinos can be either Dirac or Majorana, depending on the structure of the
scalar potential. 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; in particular, in the scenario presented there are 7 tiny
extra dimensions.
