  We investigate the embedding of brane inflation into stable compactifications
of string theory. At first sight a warped compactification geometry seems to
produce a naturally flat inflaton potential, evading one well-known difficulty
of brane-antibrane scenarios. Careful consideration of the closed string moduli
reveals a further obstacle: superpotential stabilization of the
compactification volume typically modifies the inflaton potential and renders
it too steep for inflation. We discuss the non-generic conditions under which
this problem does not arise. We conclude that brane inflation models can only
work if restrictive assumptions about the method of volume stabilization, the
warping of the internal space, and the source of inflationary energy are
satisfied. We argue that this may not be a real problem, given the large range
of available fluxes and background geometries in string theory.
