  Progress in determining the spectrum of excited baryons and mesons in lattice
QCD is described. Large sets of carefully-designed hadron operators have been
studied and their effectiveness in facilitating the extraction of excited-state
energies is demonstrated. A new method of stochastically estimating the
low-lying effects of quark propagation is proposed which will allow reliable
determinations of temporal correlations of single-hadron and multi-hadron
operators.
