  We provide results for the spectrum of scalar and pseudoscalar glueballs in
pure Yang-Mills theory using a parameter-free fully self-contained truncation
of Dyson-Schwinger and Bethe-Salpeter equations. The only input, the scale, is
fixed by comparison with lattice calculations. We obtain ground state masses of
$1.9\,\text{GeV}$ and $2.6\,\text{GeV}$ for the scalar and pseudoscalar
glueballs, respectively, and $2.6\,\text{GeV}$ and $3.9\,\text{GeV}$ for the
corresponding first excited states. This is in very good quantitative agreement
with available lattice results. Furthermore, we predict masses for the second
excited states at $3.7\,\text{GeV}$ and $4.3\,\text{GeV}$. The quality of the
results hinges crucially on the self-consistency of the employed input. The
masses are independent of a specific choice for the infrared behavior of the
ghost propagator providing further evidence that this only reflects a
nonperturbative gauge completion.
