  We derive a microscopic bound on the maximal field variation of the inflaton
during warped D-brane inflation. By a result of Lyth, this implies an upper
limit on the amount of gravitational waves produced during inflation. We show
that a detection at the level $r > 0.01$ would falsify slow roll D-brane
inflation. In DBI inflation, detectable tensors may be possible in special
compactifications, provided that $r$ decreases rapidly during inflation. We
also show that for the special case of DBI inflation with a quadratic
potential, current observational constraints imply strong upper bounds on the
five-form flux.
