  Ultracold molecules offer a broad variety of applications, ranging from
metrology to quantum computing. However, forming "real" ultracold molecules,
{\it i.e.} in deeply bound levels, is a very difficult proposition. Here, we
show how photoassociation in the vicinity of a Feshbach resonance enhance
molecular formation rates by several orders of magnitude. We illustrate this
effect in heteronuclear systems, and find giant rate coefficients even in
deeply bound levels. We also give a simple analytical expression for the
photoassociation rates, and discuss future applications of the Feshbach
Optimized Photoassociation, or FOPA, technique.
