An exact solution of Eilenberger's equations for a superconducting microbridge in the limit a VM LS TH xi //0, a VM LS TH l is given (a is the radius of the constriction between the superconductors, l is the mean free path and xi //0 is the coherence length). The current is independent of the ratio between l xi //0 and is expressed in terms of the contact resistance in the normal state. When T equals 0, the magnitude of the critical current exceeds the critical current of the tunnel contact with the same resistance, by a factor of two.