We systematically explore the parameter space of the state-of-the-art brane-antibrane inflation model (Baumann et al.) which is most rigorously derived from string theory, applying the COBE normalization and constraints on the spectral index. We define an effective volume in parameter space consistent with the constraints, and show that the fine tuning problem is this model is alleviated by four orders of magnitude for the optimal parameter values, relative to a fiducial point which has previously been considered. We also discuss the overshooting problem in this model which restricts the allowed initial conditions on the brane-antibrane separation, showing that the allowed region is expanded (by a factor of 5) when optimal model parameters are chosen. We point out a subtlety for getting correct predictions in the approximation of effective single field inflation, where the Kahler modulus is integrated out.