  We discuss Fayet-Iliopoulos terms in the context of five-dimensional
supergravity compactified on an orbifold. For this purpose we use our
superfield formulation of the off-shell 5D SUGRA. In the case of tuned FI
terms, contrary to other claims, we find BPS solutions which ensure that N=1
supersymmetry is unbroken also in warped geometries. As in the rigid case, the
FI terms induce odd masses for charged hypermultiplets, leading to the
(de)localisation of the KK wave-functions near the fix-point branes. In the
case of ungauged U(1)_R symmetry, we present also supersymmetric warped
solutions in the presence of non-trivial profiles of charged hyperscalars.
