  We consider a class of warped higher dimensional brane models with topology
$M \times \Sigma \times S^1/Z_2$, where $\Sigma$ is a $D_2$ dimensional
manifold. Two branes of codimension one are embedded in such a bulk space-time
and sit at the orbifold fixed points. We concentrate on the case where an
exponential warp factor (depending on the distance along the orbifold)
accompanies the Minkowski $M$ and the internal space $\Sigma$ line elements. We
evaluate the moduli effective potential induced by bulk scalar fields in these
models, and we show that generically this can stabilize the size of the extra
dimensions. As an application, we consider a scenario where supersymmetry is
broken not far below the cutoff scale, and the hierarchy between the
electroweak and the effective Planck scales is generated by a combination of
redshift and large volume effects. The latter is efficient due to the shrinking
of $\Sigma$ at the negative tension brane, where matter is placed. In this
case, we find that the effective potential can stabilize the size of the extra
dimensions (and the hierarchy) without fine tuning provided that the internal
space $\Sigma$ is flat.
