  We consider a broadcast channel with 3 receivers and 2 messages (M0, M1)
where two of the three receivers need to decode messages (M0, M1) while the
remaining one just needs to decode the message M0. We study the best known
inner and outer bounds under this setting, in an attempt to find the
deficiencies with the current techniques of establishing the bounds. We produce
a simple example where we are able to explicitly evaluate the inner bound and
show that it differs from the general outer bound. For a class of channels
where the general inner and outer bounds differ, we use a new argument to show
that the inner bound is tight.
