  The current observations seem to suggest that the universe has a positive
cosmological constant of the order of $H_0^2$ while the most natural value for
the cosmological constant will be $L_P^{-2}$ where $L_P = (G\hbar/c^3)^{1/2}$
is the Planck length. This reduction of the cosmological constant from
$L_P^{-2} $ to $L_P^{-2}(L_PH_0)^2$ may be interpreted as due to the ability of
quantum micro structure of spacetime to readjust itself and absorb bulk vacuum
energy densities. Being a quantum mechanical process, such a cancellation
cannot be exact and the residual quantum fluctuations appear as the ``small''
cosmological constant. I describe the features of a toy model for the spacetime
micro structure which could allow for the bulk vacuum energy densities to be
canceled leaving behind a small residual value of the the correct magnitude.
Some other models (like the ones based on canonical ensemble for the four
volume or quantum fluctuations of the horizon size) lead to an insignificantly
small value of $H_0^2(L_PH_0)^n$ with $n=0.5-1$ showing that obtaining the
correct order of magnitude for the residual fluctuations in the cosmological
constant is a nontrivial task, becaue of the existence of the small
dimensionless number $H_0L_P$ .
