  We say that a countable discrete group $G$ is {\em almost Ornstein} if for
every pair of standard non-two-atom probability spaces $(K,\kappa),
(L,\lambda)$ with the same Shannon entropy, the Bernoulli shifts $G \cc
(K^G,\kappa^G)$ and $G \cc (L^G,\lambda^G)$ are isomorphic.
