Cosmological constant and Brane New World

The estimation of the cosmological constant in inflationary Brane New World models is done. It is shown that basically it is quite large, of the same order as in anomaly-driven inflation. However, for some fine-tuning of bulk gravitational constant and AdS scale parameter $l^2$ it may be reduced to sufficiently small value. Bulk higher derivative AdS gravity with quantum brane matter may also serve as the model where small positive cosmological constant occurs.