  We consider the serve-the-longest-queue discipline for a multiclass queue
with buffers of equal size, operating under (i) the conventional and (ii) the
Halfin-Whitt heavy traffic regimes, and show that while the queue length
process' scaling limits are fully determined by the first and second order data
in case (i), they depend on finer properties in case (ii). The proof of the
latter relies on the construction of a {\it deterministic} arrival pattern.
