It has been conjectured that MWS-α scheduling policies with α going to zero are heavy-traffic optimal for scheduling in a generalized switch when the objective is to minimize the number of backlogged packets in the system. We examine this conjecture by first deriving optimal or heavy-traffic optimal policies for small switches and then comparing them to MWS- α policies by simulation. Our conclusion is that the conjecture is not true in general, i.e., there are simple topologies for which there exist policies that outperform MWS-α in heavy traffic.