  We discuss the $0^{+-}$ singlet sector of glueballs in the Klebanov-Strassler
theory. We report the results of a numerical study of the linearized equations
in the Klebanov-Strasller background and make a comparison with the spectrum of
the scalar sector. While for four towers of the total six towers of massive
pseudoscalar states our results match the spectrum of the corresponding towers
of scalars, the values for the remaining two towers diverge with those of the
scalars. We discuss possible interpretations of this divergence.
