  We analyze constraints for embedding local SU(5) F-theory GUTs into
consistent compactifications and construct explicit three-generation models
based on the geometry of arXiv:0904.3932. The key tool for studying constraints
in this problem when there is an underlying E_8 structure is the spectral
cover, which encodes all of the symmetries that fix the allowed couplings in
the superpotential, as well as the consistent, supersymmetric G-fluxes.
Imposing phenomenological requirements such as the existence of three
generations, top and bottom Yukawa couplings, good flavor structure and absence
of exotics and of a tree-level mu-term, we derive stringent constraints on the
allowed spectral covers. The resulting spectral covers are in conflict with the
neutrino scenarios that have been studied in local F-theory models unless we
allow for the possibility of additional charged fields, perhaps playing the
role of gauge messengers, that do not comprise complete GUT multiplets. Quite
remarkably, the existence of additional incomplete GUT multiplets below the GUT
scale is necessary for consistency with gauge coupling "unification", as their
effect on weak scale couplings can precisely cancel that of the internal
hypercharge flux, which distorts the gauge couplings already at M_GUT.
