  We examine brane-world scenarios in which all the observed Standard Model
particles reside on a brane but the Higgs is an elementary extra-dimensional
scalar in the bulk. We show that, for codimension 2 branes, often-neglected
interactions between the bulk Higgs and the branes cause two novel effects.
First, they cause <H> to depend only logarithmically on the UV-sensitive
coefficient, m_B^2, of the mass term, m_B^2 H^*H, of the bulk potential, thus
providing a new mechanism for tackling the hierarchy problem. Second, the Higgs
brane couplings cause the lowest mass KK mode to localize near the brane
without any need for geometrical effects like warping. We explore some
preliminary implications such models have for the Higgs signature at the LHC,
both in the case where the extra dimensions arise at the TeV scale, and in ADD
models having Large Extra Dimensions. Novel Higgs features include couplings to
fermions which can be different from Standard Model values, m_f/v, despite the
fermions acquiring their mass completely from the Higgs expectation value.
