  The Jacobian $J$ of a complete, smooth, connected curve $X$ admits a
canonical divisor $\Theta$, called the Theta divisor. It is well-known that
$\Theta$ is ample and, in fact, $3\Theta$ is very ample. For a general
complete, integral curve $X$, D'Souza constructed a compactification $\bar J$
of the Jacobian $J$ by considering torsion-free, rank 1 sheaves on $X$.
Soucaris and the author considered independently the analogous Theta divisor
$\Theta$ on $\bar J$, and showed that $\Theta$ is ample. In this article, we
show that $n\Theta$ is very ample for $n$ greater or equal to a specified lower
bound. If $X$ has at most ordinary nodes or cusps as singularities, then our
lower bound is 3. Our main tool is to use theta sections associated to vector
bundles on $X$ to embed $\bar J$ into a projective space.
