  We consider the following question: Which parameters in the extension of a
rational pleating ray across the boundary of $\Cal M$, the Maskit embedding of
the Teichm\"uller space of once punctured tori correspond to a Kleinian group?
Using methods of Keen and Series and Wright we prove a local result, stating
that on each rational ray there is a sequence of parameters in $\overline\Bbb
H\setminus\Cal M$ accumulating at the boundary point of $\Cal M$ on the ray.
These are the unique parameters on the extended $p/q$ ray for which the special
word $W_{p/q}$ is a primitive elliptic M\"obius transformation. We also show
that the discrete groups with elliptic elements in the complement of
$\overline{\Cal M}$ are boundary groups of deformation spaces of certain
Kleinian groups representing a punctured torus on their invariant component.
