  This paper explores an old problem, {\em Byzantine fault-tolerant Broadcast}
(BB), under a new model, {\em selective broadcast model}. The new model
"interpolates" between the two traditional models in the literature. In
particular, it allows fault-free nodes to exploit the benefits of a broadcast
channel (a feature from reliable broadcast model) and allows faulty nodes to
send mismatching messages to different neighbors (a feature from point-to-point
model) simultaneously. The {\em selective broadcast} model is motivated by the
potential for {\em directional} transmissions on a wireless channel.
  We provide a collection of results for a single-hop wireless network under
the new model. First, we present an algorithm for {\em Multi-Valued} BB that is
order-optimal in bit complexity. Then, we provide an algorithm that is designed
to achieve BB efficiently in terms of message complexity. Third, we determine
some lower bounds on both bit and message complexities of BB problems in the
{\em selective broadcast model}. Finally, we present a conjecture on an "exact"
lower bound on the bit complexity of BB under the {\em selective broadcast}
model.
