We describe a magnetic model with short-range couplings and an infinite-ranged Ising coupling whose strength is Gaussian distributed about zero. We show within the replica method that the model has a spin-glass transition temperature Tg which always lies above the magnetic transition temperature Tc0 of the short-range Hamiltonian taken alone, as long as the dimension d<4-2η where the exponent η describes the spin-spin correlation function for the short-range system. Two methods for computing the properties of the model are described, namely, systematic corrections to a uniform-field approximation and an expansion in the Edwards-Anderson order parameter q. Both give qualitatively similar results. We discuss evidence that the magnetization is always zero for all temperatures in this model. The model is qualitatively consistent with experiments on KMnxZn1-xF3 and EuxSr1-xS if peaks which have been attributed to Bragg scattering are actually very narrow diffuse-scattering peaks, as recent experiments on EuxSr1-xS seem to suggest.