  The reduction of the energy gap due to Landau level mixing, characterized by
the dimensionless parameter $\lambda = (e^2/\epsilon l_0)/\hbar\omega_c$, has
been calculated by variational Monte Carlo for the fractional quantum Hall
effect at filling fractions $\nu=1/3$ and 1/5 using a modified version of
Jain's composite fermion wave functions. These wave functions exploit the
Landau level mixing already present in composite fermion wave functions by
introducing a partial Landau level projection operator. Results for the energy
gaps are consistent with experimental observations in $n$-type GaAs, but we
conclude that Landau level mixing alone cannot account for the significantly
smaller energy gaps observed in $p$-type systems.
