Constraints on Wrapped DBI Inflation in a Warped Throat

We derive constraints on the tensor to scalar ratio and on the background charge of the warped throat for DBI inflation driven by D5- and D7-branes wrapped over cycles of the throat. It is shown that the background charge well beyond the known maximal value is required in most cases for DBI inflation to generate cosmological observables compatible with the WMAP3 data. Most of the results derived in this paper are insensitive to the details of the inflaton potential, and could be applied to generic warped throats.