It is well known that for any exotic pair of simply connected closed oriented 4-manifolds, one is obtained from the other by twisting a compact contractible submanifold via an involution on the boundary. By contrast, here we show that for each positive integer n, there exists a simply connected closed oriented 4-manifold X such that, for any compact (not necessarily connected) codimension zero submanifold W with b 1 (∂W ) < n, the set of all smooth structures on X cannot be generated from X by twisting W and varying the gluing map. As a corollary, we show that there exists no 'universal' compact 4-manifold W such that, for any simply connected closed 4-manifold X, the set of all smooth structures on X is generated from a 4-manifold by twisting a fixed embedded copy of W and varying the gluing map. Moreover, we give similar results for surgeries.