  Highlights in the search for nonconventional (non qqbar) meson states are the
pi_1(1400) and pi_1(1600) exotic candidates. Should they exist, mounting
theoretical arguments suggest that they are tetraquark molecular resonances
excitable by meson rescattering.
  We report a new tetraquark calculation within a model field theory
approximation to Quantum Chromodynamics in the Coulomb gauge supporting this
conjecture. We also strengthen this claim by consistently contrasting results
with exotic state predictions for hybrid (q qbar g) mesons within the same
theoretical framework.
  Our findings confirm that molecular-like configurations involving two color
singlets (a resonance, not a bound state) are clearly favored over hybrid or
color-exotic tetraquark meson (q qbar q qbar atoms) formation.
  Finally, to assist needed further experimental searches we document a useful
off-plane correlator for establishing the structure of these exotic systems
along with similar, but anticipated much narrower, states that should exist in
the charmonium and bottomonium spectra.
