We study query order within the polynomial hierarchy. P C:D denotes the class of languages computable by a polynomial-time machine that is allowed one query to C followed by one query to D HHW]. We prove that the levels of the polynomial hierarchy are order-oblivious: P p j :: p k = P p k :: p j. 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.