The spectrum of glueballs below 4 GeV in the SU(3) pure-gauge theory is inv
estigated using Monte Carlo simulations of gluons on several anisotropic la
ttices with spatial grid separations ranging from 0.1 to 0.4 fm. Systematic
errors from discretization and finite volume are studied, and the continuu
m spin quantum numbers are identified. Care is taken to distinguish single
glueball states from two-glueball and torelon-pair states. Our determinatio
n of the spectrum significantly improves upon previous Wilson action calcul
ations. [S0556-2821(99)07013-7].