  We consider the Type IIB string theory in the presence of various extra
$7/\bar 7$-brane pairs compactified on a warped Calabi-Yau threefold that
admits a conifold singularity. We demonstrate that the volume modulus can be
stabilized perturbatively at a non-supersymmetric $AdS_4/dS_4$ vacuum by the
effective potential that includes the stringy $(\alpha^\prime)^3$ correction
obtained by Becker {\it et al.} together with a combination of positive tension
and anomalous negative tension terms generated by the additional
7-brane-antibrane pairs.
