  For a class of mixed two -qubit states we show that it is not possible to
discriminate between states violating or non - violating Bell - CHSH
inequalities, knowing only their entanglement and mixedness. For a large set of
possible values of these quantities, we construct pairs of states with the same
entanglement and mixedness such that one state is violating but the other is
non - violating Bell - CHSH inequality.
