  We introduce a new variational wavefunction for a quantum Hall bilayer at
total filling $\nu = 1$, which is based on $s$-wave BCS pairing between
composite-fermion electrons in one layer and composite-fermion holes in the
other. We compute the overlap of the optimized trial function with the ground
state from exact diagonalization calculations of up to 14 electrons in a
spherical geometry, and we find excellent agreement over the entire range of
values of the ratio between the layer separation and the magnetic length. The
trial wavefunction naturally allows for charge imbalance between the layers and
provides important insights into how the physics at large interlayer
separations crosses over to that at small separations in a fashion analogous to
the BEC-BCS crossover.
