  We address the problem of the cosmological constant within the
Randall-Sundrum scenario with a brane stabilization mechanism. We consider
brane tensions of general form. We examine the conditions under which a small
change of the positive tension of the first brane can be absorbed in a small
modification of the two-brane configuration, instead of manifesting itself as a
cosmological constant. We demonstrate that it is possible to have a
cosmological constant in the range predicted by recent observational data, if
there is an ultraviolet cutoff of order 10 TeV in the contributions to the
brane tension from vacuum fluctuations.
