  We present a non-perturbative canonical analysis of the D=3
quadratic-curvature, yet ghost-free, model to exemplify a novel, "constraint
bifurcation", effect. Consequences include a jump in excitation count: a
linearized level gauge variable is promoted to a dynamical one in the full
theory. We illustrate these results with their concrete perturbative
counterparts. They are of course mutually consistent, as are perturbative
findings in related models. A geometrical interpretation in terms of
propagating torsion reveals the model's relation to an (improved) version of
Einstein-Weyl gravity at the linearized level. Finally, we list some necessary
conditions for triggering the bifurcation phenomenon in general interacting
gauge systems.
