  We study the phases of the 1+1 dimensional Non-Commutative Open String theory
on a circle. We find that the length scale of non-commutativity increases at
strong coupling, the coupling in turn being dressed by a power of D-string
charge. The system is stringy at around this length scale, with dynamics
involving an interplay between the open and wrapped closed strings sectors.
Above this energy scale and at strong coupling, and below it at weak coupling,
the system acquires a less stringy character. The near horizon geometry of the
configuration exhibits several intriguing features, such as a flip in the
dilaton field and the curvature scale, reflecting UV-IR mixing in
non-commutative dynamics. Two special points in the parameter measuring the
size of the circle are also identified.
