  In this paper we study fractional quantum Hall composite fermion
wavefunctions at filling fractions \nu = 2/3, 3/5, and 4/7. At each of these
filling fractions, there are several possible wavefunctions with different spin
polarizations, depending on how many spin-up or spin-down composite fermion
Landau levels are occupied. We calculate the energy of the possible composite
fermion wavefunctions and we predict transitions between ground states of
different spin polarizations as the ratio of Zeeman energy to Coulomb energy is
varied. Previously, several experiments have observed such transitions between
states of differing spin polarization and we make direct comparison of our
predictions to these experiments. For more detailed comparison between theory
and experiment, we also include finite-thickness effects in our calculations.
We find reasonable qualitative agreement between the experiments and composite
fermion theory. Finally, we consider composite fermion states at filling
factors \nu = 2+2/3, 2+3/5, and 2+4/7. The latter two cases we predict to be
spin polarized even at zero Zeeman energy.
