We discuss special isothermic nets of type , a new class of discrete isothermic nets, generalizing isothermic nets with constant mean curvature in spaceforms. In the case these are the discrete analogues of Bianchi's special isothermic surfaces that can be regarded as the origin of the rich transformation theory of isothermic surfaces. Accordingly, special isothermic nets come with Backlund transformations and a Lawson correspondence. The notion of complementary nets naturally occurs and sheds further light on the relation between geometry and integrability.