Earlier work with Robert Gompf and Abigail Thompson classified, via a natural slope indexed by the rationals, all two-component links which contain the square knot and from which (S^1 times S^2) # (S^1 times S^2) can be obtained by surgery. It was argued there that each of a certain family L_n of such links probably contradicts the Generalized Property R Conjecture. Left unresolved was how the family L_n fits into the classification scheme. This question is resolved here, in part by giving varied perspectives and more detail on the construction of the L_n.