  We propose a measure of the stability of composite fermions (CF's) at
even-denominator Landau-level filling fractions. Assuming Landau-level mixing
effects are not strong, we show that the CF liquid at $\nu=2+1/2$ in the $n=1$
Landau level cannot exist and relate this to the absence of a hierarchy of
incompressible states for filling fractions $2+1/3 < \nu < 2+2/3$. We find that
a polarized CF liquid should exist at $\nu=2+1/4$. We also show that, for CF
states, the variation with system size of the ground state energy of
interacting electrons follows that for non-interacting particles in zero
magnetic field. We use this to estimate the CF effective masses.
