  We solve the Faddeev bound-state equations for three particles with simple
two-body nonlocal, separable potentials that yield a scattering length twice as
large as a positive effective range, as indicated by some lattice QCD
simulations. Neglecting shape parameters, the two-body bound state is a double
pole. For bosons we obtain a correlation between three- and two-body energies.
For nucleons, this correlation depends additionally on the ratio of effective
ranges in the two two-body $S$-wave channels. When this ratio takes the value
suggested by lattice QCD, our three-body energy agrees well with a direct
lattice determination. When this ratio takes the experimental value, we find a
three-body bound state with energy close to that of the physical triton. We
suggest that results could be improved systematically with distorted-wave
perturbation theory around a separable potential whose form factor is an
inverse square root of momentum squared.
