The mass spectrum of a meson-meson system in compact three-dimensional
lattice quantum electrodynamics is computed from a time correlation m
atrix with staggered fermions. The energy levels indicate a slightly a
ttractive residual interaction between the mesons. From the finite-vol
ume spectrum scattering phase shifts within the various irreducible re
presentations of the (cubic, d = 2) lattice symmetry group are extract
ed. The s-wave (l = 0) phase shifts are consistent with repulsion at s
mall relative distance. The d-wave (l = 2) data indicate intermediate-
range attraction.