Motivated by the discovery of extremely low-energy collective modes in the
fractional quantum Hall effect [Kang, Pinczuk et al., Phys. Rev. Lett. 84,
546 (2000)], with energies below the Zeeman energy, we study theoretically
thr spin-reversed excitations for fractional quantum Hall states at v= 2/5
and 3/7 and find qualitatively different behavior than for v= 1/3. We find
that a low-energy, charge-neutral ''spin roton," associated with spin-rever
sed excitations that involve a change in the composite-fermion Landau level
index, has energy in reasonable agreement with experiment.