The coupled-cluster method is a very powerful method of quantum many-body theory which has recently been applied to Hamiltonian formulations of lattice gauge field theories. Previous calculations in the U(1) model in 2+1 dimensions have employed a local approximation scheme in which only correlations between adjacent plaquettes are taken into account. Here, we extend these calculations to include longer-ranged two-plaquette correlations, and also apply the local approximation scheme to the U(1) model in 3+1 dimensions. ((orig.)).