The theory proposed is an extension of the constrained-junction theory of Flory and Erman and the subsequent constrained-chain theory of Erman and Monnerie. As in these earlier theories, the elastic free energy Delta A(el) is calculated as the sum Delta A(el) = Delta A(ph) + Delta A(c), where Delta A(ph) is the contribution for a phantom network, and the additional term Delta A(c) is due to the effects of constraints on fluctuations. Instead of allowing the constraints to affect the fluctuations of only the junctions or the centers of mass of the network chains, however, the constraints are now applied continuously along the chains. The results of illustrative calculations on this "diffused-constraint" model are compared with the corresponding results from the earlier theories.