The smooth version of the 4-dimensional Poincare Conjecture (S4PC) states that every homotopy 4-sphere is diffeomorphic to the standard 4-sphere.  One way to attack the S4PC is to examine a restricted class of 4-manifolds.  For example, Gabai’s proof of Property R implies that every homotopy 4-sphere built with one 2-handle and one 3-handle is standard.  In this talk, we consider homotopy 4-spheres X built with two 2-handles and two 3-handles, which are uniquely determined by the attaching link L for the 2-handles in the 3-sphere.  We prove that if one of the components of L is the connected sum of a torus knot T(p,2) and its mirror (a generalized square knot), then X is diffeomorphic to the standard 4-sphere.  This is joint work with Jeffrey Meier.