  Following some recent work by Gross, we consider the partition function for
QCD on a two dimensional torus and study its stringiness. We present strong
evidence that the free energy corresponds to a sum over branched surfaces with
small handles mapped into the target space. The sum is modded out by all
diffeomorphisms on the world-sheet. This leaves a sum over disconnected classes
of maps. We prove that the free energy gives a consistent result for all smooth
maps of the torus into the torus which cover the target space $p$ times, where
$p$ is prime, and conjecture that this is true for all coverings. Each class
can also contain integrations over the positions of branch points and small
handles which act as ``moduli'' on the surface. We show that the free energy is
consistent for any number of handles and that the first few leading terms are
consistent with contributions from maps with branch points.
