  Common smoothness indicators used in Weighted Essentially
Non\--Os\-cil\-la\-to\-ry (WENO) reconstructions [Jiang, G.S., Shu, C.W.:
Efficient implementation of {Weighted} {ENO} schemes, J.\ Comput.\ Phys.
\textbf{126}, 202--228 (1996)] have quadratic cost with respect to the order. A
set of novel smoothness indicators with linear cost of computation with respect
to the order is presented. These smoothness indicators can be used in the
context of schemes of the type introduced by Yamaleev and Carpenter [Yamaleev,
N.K., Carpenter, M.H.: A systematic methodology to for constructing high-order
energy stable WENO schemes. J. Comput. Phys. \textbf{228}(11), 4248-4272
(2009)]. The accuracy properties of the resulting non-linear weights are the
same as those arising from using the traditional Jiang-Shu smoothness
indicators in Yamaleev-Carpenter-type reconstructions. The increase of the
efficiency and ease of implementation are shown.
