  We investigate recent claims that brane inflation solves the overshoot
problem through a combination of microphysical restrictions on the phase space
of initial conditions and the existence of the Dirac-Born-Infeld (DBI)
attractor in regimes where the slow-roll attractor does not apply. Carrying out
a comprehensive analysis of the parameter space allowed by the latest advances
in brane inflation model-building, we find that these restrictions are
insufficient to solve the overshoot problem. The vast majority of the phase
space of initial conditions is still dominated by overshoot trajectories. We
present an analytic proof that the brane-inflationary attractor must be close
to the slow-roll limit, and update the predictions for observables such as
non-Gaussianity, cosmic string tension and tensor modes.
