  Progress in computing the spectrum of excited baryons and mesons in lattice
QCD is described. Large sets of spatially-extended hadron operators are used.
The need for multi-hadron operators in addition to single-hadron operators is
emphasized, necessitating the use of a new stochastic method of treating the
low-lying modes of quark propagation which exploits Laplacian Heaviside
quark-field smearing. A new glueball operator is tested and computing the
mixing of this glueball operator with a quark-antiquark operator and multiple
two-pion operators is shown to be feasible. Some of our initial results show
warning signs about extracting high-lying resonance energies using only
single-hadron operators.
