  We provide numerical evidence that a p_{x}-i p_{y} paired
Bonderson--Slingerland (BS) non-Abelian hierarchy state is a strong candidate
for the observed nu=12/5 quantum Hall plateau. We confirm the existence of a
gapped incompressible nu = 12/5 quantum Hall state with shift S=2 on the
sphere, matching that of the BS state. The exact ground state of the Coulomb
interaction at S=2 is shown to have large overlap with the BS trial wave
function. Larger overlaps are obtained with BS-type wave functions that are
hierarchical descendants of general p_{x}-i p_{y} weakly-paired states at
nu=5/2. We perform a finite size scaling analysis of the ground state energies
for nu=12/5 states at shifts corresponding to the BS (S=2) and 3-clustered
Read-Rezayi (S=-2) universality classes. This analysis reveals very tight
competition between these two non-Abelian topological orders.
