  We present extensive comparisons of the composite fermion theory with exact
results in the filling factor range $2/5>\nu>1/3$, which affirm that the
composite fermion theory correctly describes the qualitative reorganization of
the low energy Hilbert space of the strongly correlated electrons, and predicts
eigenenergies with an accuracy of $\sim 0.1$ %. These facts establish the basic
validity of the composite fermion description in this filling factor region.
