It is now well known that some 'spontaneously broken gauge theories' do not exhibit a true phase transition. The electroweak theory for example has only a crossover for Higgs mass larger than about 100 GeV. We conjecture, however, that a true phase transition does occur whenever the theory exhibits topologically stable defects. To test this idea, we have developed a non-perturbative formalism for measuring defect free energies (monopole mass or vortex tension), initially in three-dimensional SU(2)+adjoint Higgs models. Starting from twisted, translation invariant boundary conditions, we perform a change of variables that allows us to express the defect free energies in terms of 't Hooft loops. We propose that the defect free energies can be used to distinguish between phases in this model, and also more generally in other gauge field theories where no local order parameters exist. Preliminary results of a simulation will be presented.