  We propose a pair-condensate variational approach (PCV) to determine a set of
the most important collective pairs in the description of low-lying states in
atomic nuclei. Having available the precise details on these key collective
pairs -- their spin, parity, and structure -- can be particularly useful in
calculations based on the nucleon-pair approximation (NPA), helping to reduce
their uncertainties. In trial calculations for the transitional Ba isotopes,
our variational approach describes the evolution of quadrupole-deformation
properties similar to Hartree-Fock treatments, while at the same time
highlighting the $\gamma$ softness of $^{132}$Ba. Our approach can conclusively
determine which collective pairs are critical for obtaining the lowest possible
yrast, quasi-beta, quasi-gamma bands, producing both the level structure of
these bands and related B(E2) values in reasonable consistency with experiment.
These trial calculations suggest that with our PCV approach the NPA can be
meaningfully applied to transitional nuclei with a wide spectrum of shapes. We
also show that while neutron negative-parity pairs could in principle have an
important impact on backbending in $^{132}$Ba, they are not favored for this
nucleus.
