  We investigate whether explicit models of warped D-brane inflation are
possible in string compactifications. To this end, we study the potential for
D3-brane motion in a warped conifold that includes holomorphically-embedded
D7-branes involved in moduli stabilization. The presence of the D7-branes
significantly modifies the inflaton potential. We construct an example based on
a very simple and symmetric embedding due to Kuperstein, z_1 = constant, in
which it is possible to fine-tune the potential so that slow roll inflation can
occur. The resulting model is rather delicate: inflation occurs in the vicinity
of an inflection point, and the cosmological predictions are extremely
sensitive to the precise shape of the potential.
