  In this paper we consider the Skorokhod embedding problem for general
starting and target measures. In particular, we provide necessary and
sufficient conditions for a stopping time to be minimal in the sense of
Monroe(1972). The resulting conditions have a nice interpretation in the
graphical picture of Chacon and Walsh. Further, we demonstrate how the
construction of Chacon and Walsh can be extended to any (integrable) starting
and target distributions, allowing the constructions of Azema-Yor, Vallois and
Jacka to be viewed in this context, and thus extended easily to general
starting and target distributions. In particular, we describe in detail the
extension of the Azema-Yor embedding in this context, and show that it retains
its optimality property.
