The spectrum of bound states of gluons is discussed within the MIT bag model. We argue that (1) contrary to previous analysis there is no light exotic 1−+ state in the two gluon sector, (2) experiments on the three gluon sector can clearly differentiate the bag model from other models, (3) the state seen in J/ψ radiative decays at 1.4 GeV is most likely a pseudoscalar glueball, and (4) there should be a second 2++ state underneath the f(1270) resonance.