  We prove the quenched version of the central limit theorem for the
displacement of a random walk in doubly stochastic random environment, under
the $H_{-1}$-condition, with slightly stronger, $L^{2+\varepsilon}$ (rather
than $L^2$) integrability condition on the stream tensor. On the way we extend
Nash's moment bound to the non-reversible, divergence-free drift case.
