  We apply a new self-tuning mechanism to the well-known
Kachru-Kallosh-Linde-Trivedi (KKLT) model to address the cosmological constant
problem. In this mechanism the cosmological constant $\lambda$ contains a
supersymmetry breaking term ${\mathcal E}_{\rm SB}$ besides the usual scalar
potential ${\mathcal V}_{\rm scalar}$ of the $N=1$ supergravity, which is
distinguished from the usual theories where $\lambda$ is directly identified
with ${\mathcal V}_{\rm scalar}$ alone. Also in this mechanism, whether
$\lambda$ vanishes or not is basically determined by the tensor structure of
the scalar potential density, not by the zero or nonzero values of the scalar
potential itself. As a result of this application we find that the natural
scenario for the vanishing $\lambda$ of the present universe is to take one of
the AdS (rather than dS) vacua of KKLT as the background vacuum of our present
universe. This AdS vacuum scenario has more nice properties as compared with dS
vacua of the usual flux compctifications. The background vacuum is stable both
classically and quantum mechanically (no tunneling instabilities), and the
value $\lambda =0$ is also stable against quantum corrections because in this
scenario the perturbative corrections of ${\mathcal V}_{\rm scalar}$ and
quantum fluctuations $\delta_Q {\hat I}_{\rm brane}^{(NS)} + \delta_Q {\hat
I}_{\rm brane}^{(R)}$ on the branes are all gauged away by an automatic
cancelation between ${\mathcal V}_{\rm scalar} + \delta_Q {\hat I}_{\rm
brane}^{(NS)} + \delta_Q {\hat I}_{\rm brane}^{(R)}$ and ${\mathcal E}_{\rm
SB}$.
