  We discuss E3-brane instantons in N=1 F-theory compactifications to four
dimensions and clarify the structure of E3-E3 zero modes for general
world-volume fluxes. We consistently incorporate SL(2,Z) monodromies and
highlight the relation between F-theory and perturbative IIB results. We
explicitly show that world-volume fluxes can lift certain fermionic zero-modes,
whose presence would prevent the generation of non-perturbative superpotential
terms, and we discuss in detail the geometric interpretation of the zero-mode
lifting mechanism. We provide a IIB derivation of the index for generation of
superpotential terms and of its modification to include world-volume fluxes,
which reproduces and generalizes available results. We apply our general
analysis to the explicit, though very simple, example of compactification on
P^3 and its orientifold weak-coupling limit. In particular, we provide an
example in which a non-rigid divisor with fluxes contributes to the
superpotential.
