There has been much theoretical discussion of the confinement of the radio jets associated with extragalactic radio sources. There are now several examples of sources where the minimum pressure inferred in the jets appears to exceed the external gas pressure, which suggests that magnetic pinching may be playing an important part in the confinement. This issue has been highlighted by recent remarkable observations, using the Very Large Array, of the radio lobes associated with the galactic X-ray source Sco X-1 by Fomalont et al. We argue here that these results necessitate magnetic focusing and that this also strengthens the case for magnetic focusing in the extragalactic sources. We show that a sufficient overpressure with respect to the ambient interstellar medium can be achieved if the radius of the jet is reduced by a factor 10–100, and the converging flow becomes dissipative. The radio lobes which form at that point quickly die out again due to electron expansion losses in the now rapidly diverging jet. On the basis of this model it is predicted that the Faraday rotation changes sign across the radio lobes, and that the shape of the lobes should be conical with the apex pointing towards Sco X-1.