  Among the inflationary models based on string theory, the D3/D7 model has the
advantage that the flatness of the inflaton potential can be protected even
with moduli stabilization. However, the Abrikosov-Nielsen-Olesen BPS cosmic
strings produced at the end of original D3/D7 inflation lead to an additional
contribution to the CMB anisotropy. To make this contribution consistent with
the WMAP results one needs an extremely small gauge coupling in the effective
D-term inflation model. Such couplings may be difficult to justify in string
theory. Here we develop a generalized version of the D3/D7 brane model, which
leads to semilocal strings, instead of the topologically stable ANO cosmic
strings. We show that the semilocal strings have unbroken supersymmetry when
embedded into supergravity with FI terms. The energy of these strings is
independent of their thickness. We confirm the existing arguments that strings
of such type disappear soon after their formation and do not pose any
cosmological problems, for any value of the gauge coupling. This should
simplify the task of constructing fully realistic models of D3/D7 inflation.
