  The cosmological constant problem is how one chooses, without fine-tuning,
one singular point $\Lambda_{eff}=0$ for the 4D cosmological constant. We argue
that some recently discovered {\it weak self-tuning} solutions can be viewed as
blowing-up this one point into a band of some parameter. These weak self-tuning
solutions may have a virtue that only de Sitter space solutions are allowed
outside this band, allowing an inflationary period. We adopt the hybrid
inflation at the brane to exit from this inflationary phase and to enter into
the standard Big Bang cosmology.
