  We examine the possibility of creating the Moore-Read Pfaffian in the lowest
Landau level when the multicomponent Halperin 331 state (believed to describe
quantum Hall bilayers and wide quantum wells at the filling factor $\nu=1/2$)
is destroyed by the increase of tunneling. Using exact diagonalization of the
bilayer Hamiltonian with short-range and long-range (Coulomb) interactions in
spherical and periodic rectangular geometries, we establish that tunneling is a
perturbation that drives the 331 state into a compressible composite Fermi
liquid, with the possibility for an intermediate critical state that possesses
some properties of the Moore-Read Pfaffian. These results are interpreted in
the two-component BCS model for Cauchy pairing with a tunneling constraint. We
comment on the conditions to be imposed on a system with fluctuating density in
order to achieve the stable Pfaffian phase.
