  We distinguish six classes of families of locally equivalent states in a
straightforward scheme for classifying all 2-q-bit states; four of the classes
consist of two subclasses each. The simple criteria that we stated recently for
checking a given state's positivity and separability are justified, and we
discuss some important properties of Lewenstein-Sanpera decompositions. An
upper bound is conjectured for the sum of the degree of separability of a
2-q-bit state and its concurrence.
