  We study instanton effects in theories with compact extra dimensions. We
perform an instanton calculation in a 5d theory on a circle of radius R, with
gauge, scalar, and fermion fields in the bulk of the extra dimension. We show
that, depending on the matter content, instantons of size rho << R can dominate
the amplitude. Using deconstruction as an ultraviolet definition of the theory
allows us to show, in a controlled approximation, that for a small number of
bulk fermions, the amplitude for small size instantons exponentially grows as
e^{O(1)R/rho}.
