  Progress in computing the spectrum of excited baryons and mesons in lattice
QCD is described. Our first results in the zero-momentum bosonic I=1, S=0, T1u+
symmetry sector of QCD using a correlation matrix of 56 operators are
presented. In addition to a dozen spatially-extended meson operators, 44
two-meson operators are used, involving a wide variety of light isovector,
isoscalar, and strange meson operators of varying relative momenta. All needed
Wick contractions are efficiently evaluated using a stochastic method of
treating the low-lying modes of quark propagation that exploits Laplacian
Heaviside quark-field smearing. Level identification is discussed.
