  Following earlier authors, we re-examine constraints on the radial velocity
anisotropy of generic stellar systems using arguments for phase space density
positivity, stability, and separability. It is known that although the majority
of commonly used systems have an maximum anisotropy of less than half of the
logarithmic density slope \emph{i.e.} $\beta < \gamma/2$, there are exceptions
for separable models with large central anisotropy. Here we present a new
exceptional case with above-threshold anisotropy locally but with an isotropic
center nevertheless. These models are non-separable and we maintain positivity.
Our analysis suggests that regions of above-threshold anisotropy are more
related to regions of possible secular instability, which might be observed in
self-consistent galaxies in a short-lived phase. s an equilibrium solution for
a collisionless system.
