  We show that the use of higher dimensional wrapped branes can significantly
extend the inflaton field range compared to brane inflation models which use
D3-branes. We construct a simple inflationary model in terms of 5-branes
wrapping a 2-cycle and traveling towards the tip of the Klebanov-Strassler
throat. Inflation ends when the branes reach the tip of the cone and
self-annihilate. Assuming a quadratic potential for the brane it is possible to
match the CMB data in the DBI regime, but we argue that the backreaction of the
brane is important and cannot be neglected. This scenario predicts a strong
non-Gaussian signal and possibly detectable gravitational waves.
