The possibility of a bound Σ−nn system is examined in the light of recent experimental data of Dosch et al. on Σ+−p elastic scattering. A singlet Σ−−n potential that gives a bound state at zero energy, and the strongest possible triplet Σ−−n potential that is compatible with experimental data, are constructed in the Moszkowski-Scott spirit. It is concluded that a bound Σ−nn cannot exist. The lowest-order three-body forces in Σ−nn are briefly examined and it is argued that these are likely to be unimportant.