  A novel procedure is given for choosing smoothest stencil to construct less
oscillatory ENO schemes. The procedure is further used to define smoothness
parameter in the non-linear weights of new WENO schemes. The main significant
features of these new ENO and WENO schemes is that they are less oscillatory
and achieve their relevant order of accuracy in the presence of critical points
in the exact solution. It is shown theoretically as well as computationally in
$L^1$ and $L^\infty$ norm. Moreover, computational results are given to show
less oscillatory behavior of the new WENO scheme compared to WENO5-JS and
WENO5-Z schemes.
