  In theories with flux compactification in eight or higher dimensions, the
extra-dimensional components of the gauge field may be regarded as the Higgs
field candidates. We suggest a way to protect these components from getting
large tree-level masses by imposing a $Z_2$-symmetry acting on compact
manifolds and background fields on them. In our scheme the infinite series of
heavy KK modes naturally decouples from the light Higgs candidates, whose
number is generically larger than one. We also present toy models with three
families of leptons, illustrating that the Yukawa sector in our scheme is
fairly strongly constrained. In one of these models, one fermion gets a
tree-level mass after electroweak symmetry breaking, while two others remain
naturally massless at the tree level.
