  We consider right-handed neutrinos propagating in $\delta$ (large) extra
dimensions, whose only coupling to Standard Model fields is the Yukawa coupling
to the left-handed neutrino and the Higgs boson. These theories are attractive
as they can explain the smallness of the neutrino mass, as has already been
shown. We show that if $\delta$ is bigger than two, there are strong
constraints on the radius of the extra dimensions, resulting from the
experimental limit on the probability of an active state to mix into the large
number of sterile Kaluza-Klein states of the bulk neutrino. We also calculate
the bounds on the radius resulting from requiring that perturbative unitarity
be valid in the theory, in an imagined Higgs-Higgs scattering channel.
