If E/Q is an elliptic curve, and d is a squarefree integer, then the 2-torsion modules of E and its quadratic twist E_d are isomorphic. In particular their 2-Selmer groups can be made to lie in the same space. Poonen-Rains provide a heuristic model for the behaviour of these 2-Selmer groups individually, as E varies, but how independent are they? We'll present results in this direction.