  In this paper we describe a pseudoscalar subsector of the Klebanov-Strassler
model. This subsector completes the holographic reconstruction of the spectrum
of the lowest-lying glueball states, which are singlet under the global
symmetry group $SU(2)\times SU(2)$. We derive the linearized supergravity
equations for the pseudoscalar fluctuations and analyze their spectrum. The
system of equation is shown to be compatible with six eigenmodes, as expected
from supersymmetry. Our numerical analysis allows to reliably extract four of
the corresponding towers. Their values match well the eigenvalues of the
$0^{++}$ scalar states known from an earlier work. Assuming the masses of
$0^{++}$ as a reference, we compare the lightest states of the holographic
spectrum with lattice calculations in the quenched QCD at $N_c=3$ and
$N_c=\infty$.
