  Hemaspaandra, Hempel, and Wechsung [cs.CC/9909020] initiated the field of
query order, which studies the ways in which computational power is affected by
the order in which information sources are accessed. The present paper studies,
for the first time, query order as it applies to the levels of the polynomial
hierarchy. We prove that the levels of the polynomial hierarchy are
order-oblivious. Yet, we also show that these ordered query classes form new
levels in the polynomial hierarchy unless the polynomial hierarchy collapses.
We prove that all leaf language classes - and thus essentially all standard
complexity classes - inherit all order-obliviousness results that hold for P.
