  We systematically explore the parameter space of the state-of-the-art
brane-antibrane inflation model (Baumann {\it et al}., arXiv:0706.0360,
arXiv:0705.3837) which is one of the most rigorously derived from string
theory, applying the cosmic background explorer normalization and constraint on
the spectral index. We improve on previous treatments of uplifting by
antibranes and show that the contributions from noninflationary throats play an
important role in achieving a flat inflationary potential. To quantify the
degree of fine-tuning needed by the model, we define an effective volume in the
part of parameter space which is consistent with experimental constraints, and
using Monte Carlo methods to search for a set of optimal parameters, we show
that the degree of fine-tuning is alleviated by 8 orders of magnitude relative
to a fiducial point which has previously been considered. In fact, close to the
optimal parameter values, fine-tuning is no longer needed for any of the
parameters. We show that in this natural region of the parameter space, larger
values of $n_s$ close to 0.99 (still within 2$\sigma$ of the WMAP5 central
value) are favored, giving a new aspect of testability to the model.
