We describe a model for the scalar sector where all interactions occur either at an ultra-high scale A(sub U) (approx) 10(sup 16)-10(sup 19) GeV or at an intermediate scale (Lambda)(sub I) = 10(sup 9)-10(sup 11) GeV. The interaction of physics on these two scales results in an SU(2) Higgs condensate at the electroweak (EW) scale, (Lambda)(sub EW), through a seesaw-like Higgs mechanism, (Lambda)(sub EW) (approx) (Lambda)(sub 1)(sup 2)/(Lambda)(sub U), while the breaking of the SM SU(2) x U(1) gauge symmetry occurs at the intermediate scale (Lambda)(sub 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(sub (nu)) (approx) (Lambda)(sub I)(sup 4)/(Lambda)(sub U)(sup 3) (approx) (Lambda)(sub EW)(sup 2)/(Lambda)(sub U). We also show that our seesaw Higgs model can be naturally embedded, in theories with tiny extra dimensions of size R (approx) (Lambda)(sub U)(sup -1) (approx) 10(sup -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.