  We establish a new outer bound for the capacity region of product broadcast
channels. This outer bound matches Marton's inner bound for a variety of
classes of product broadcast channels whose capacity regions were previously
unknown. These classes include product of reversely semi-deterministic and
product of reversely more-capable channels. A significant consequence of this
new outer bound is that it establishes, via an example, that the previously
best known outer-bound is strictly suboptimal for the general broadcast
channel. Our example is comprised of a product broadcast channel with two
semi-deterministic components in reverse orientation.
