  The density dependence of nuclear symmetry energy remains poorly constrained.
Starting from precise empirical values of the nuclear volume and surface
symmetry energy coefficients and the nuclear saturation density, we show how in
the ambit of microscopic calculations with different energy density
functionals, the value of the symmetry energy slope parameter $L$ alongwith
that for neutron skin can be put in tighter bounds. The value of $L$ is found
to be $L$= 64$\pm $5 MeV. For $^{208}$Pb, the neutron skin thickness comes out
to be 0.188 $\pm $0.014 fm. Knowing $L$, the method can be applied to predict
neutron skins of other nuclei.
