  We present a study of the $SU(3)$ glueball spectrum for all $J^{PC}$ values
at lattice spacings down to $a^{-1}=3.73 (6)$ GeV ($\beta=6.4$) using lattices
of size up to $32^4$. We extend previous studies and show that the continuum
limit has effectively been reached. The number of clearly identified $J^{PC}$
states has been substantially increased. There are no clear signals for
spin-exotic glueballs below 3 GeV. A comparison with current experimental
glueball candidates is made.
