We consider compactifications of the recently discovered tachyon free non-supersymmetric string on tori of Lorentzian self dual lattices. The one loop cosmological constant is computed as a function of the parameters characterizing the lattices. When the lattice parameters are treated as dynamical variables, their equations of motion require extremization of A. This extremization determines the allowed gauge groups and mass spectra. We explicitly find some extremes of A, valid to all orders in perturbation theory. A very general duality relation between compactifications is demonstrated, which leads to an equivalence of compactifications on tori of radii R aud 1/R.