Kinetic simulations and analysis show that backward stimulated Raman scattering (BSRS), in regimes of large linear Landau damping of the primary Langmuir wave, attains levels greatly exceeding the predictions of models based on fixed damping. These regimes are encountered in plasma conditions expected for target designs to be fielded at the National Ignition Facility [J. D. Lindl, Inertial Confinement Fusion (Springer-Verlag, New York, 1998)]. Trapped electrons in the Langmuir wave have the dual effect of reducing its damping, thereby enhancing the BSRS response, and saturating this response by phase detuning, a consequence of the trapping-induced, time-dependent, frequency shift. BSRS, then, occurs as a train of sub-picosecond pulses, arising from the competition between phase detuning and parametric regeneration. A simple three wave parametric model, including the effect of the nonlinear frequency shift and residual nonlinear damping, reproduces these essential features. A similar scenario applies to backward stimulated Brillouin scattering (BSBS). BSRS activity many orders of magnitude above noise level is found for intense laser speckles even when the primary Langmuir wave number times the Debye length is as high as 0.55. The simulation model consistently accounts for the competition of other instabilities, including BSBS, forward stimulated Raman scattering, and the Langmuir decay instability with cavitation.