  We study various improved staggered quark Dirac operators on quenched gluon
backgrounds in lattice QCD. We find a clear separation of the spectrum of
eigenvalues into high chirality, would-be zero modes and others, in accordance
with the Index Theorem. We find the expected clustering of the non-zero modes
into quartets as we approach the continuum limit. The predictions of random
matrix theory for the epsilon regime are well reproduced. We conclude that
improved staggered quarks near the continuum limit respond correctly to QCD
topology.
