  We obtain cosmological constraints on models of inflation which exhibit rapid
roll solutions. Rapid roll attractors exist for potentials with large mass
terms and are thus of interest for inflationary model building within string
theory. We constrain a general ansatz for the power spectrum arising from rapid
roll inflation that, in the small field limit, can be associated with tree
level hybrid potentials with variable mass terms and nonminimal gravitational
coupling $\xi R\phi^2$. We consider perturbations generated through modulated
reheating and/or curvaton mechanisms in place of the observationally
unacceptable primary spectra generated by inflaton fluctuations in these
models. The lack of a hierarchy amongst higher-order $k$-dependencies of the
power spectrum results in models with potentially large runnings, allowing us
to impose tight constraints on such models using CMB and LSS data. In
particular, we find $n_s <1$ and $|\alpha| < 0.01$. We conclude with a concrete
realization of rapid roll inflation within warped throat brane inflation that
is in good agreement with current data.
