  A $T$-Schottky group is a discrete group of M\"obius transformations whose
generators identify pairs of, possibly-tangent, Jordan curves on the complex
sphere, ${\hat{\IC}}$. If the curves are Euclidean circles then the group is
termed classical $T$-Schottky. We describe the boundary of the space of
classical $T$-Schottky groups affording two parabolic generators within the
larger parameter space of all $T$-Schottky groups with two parabolic
generators. This boundary is surprisingly different from that of the larger
space. It is analytic while the boundary of the larger space appears to be
fractal. Approaching the boundary of the smaller space does not correspond to
pinching, circles necessarily become tangent but extra parabolics need not
develop. As an application we construct an explicit one parameter family of two
parabolic generator non-classical $T$-Schottky groups.
