This is the second of two talks with T. Chinburg about deformation rings which are not complete intersections. I will first discuss the connection between capping groups and deformation rings. I will then prove that every 2-dimensional irreducible representation of S_4 over a field of characteristic 2 has a universal deformation ring which is not a complete intersection. Combining this with the results from the previous week, we then get infinitely many arithmetic examples.