This paper presents further developments in the geometric design of deployable structures that are self-standing and stress-free in both the deployed and collapsed configurations. The basic geometric design philosophy of these structures has been explained in previous publications. Furthermore, guidelines for the geometric design of polygonal and trapezoidal units for flat and curved structures have been proposed. The size of the joints has been assumed to be infinitesimally small. In reality however, the joints have certain discrete dimensions that have to be taken into account. This paper presents a more realistic geometric design procedure allowing for discrete joint sizes. First, a simple but accurate model is adopted for the joints that treats them as a grid of bars that are hinged to the members of the structure. Then, the geometric constraints and deployability conditions derived earlier are modified to account for joint size. Regular polygonal units for flat and curved structures, and trapezoidal units for flat structures are covered. An example of a medium size model is presented, where adjustments for the joint size had to be made during geometric design. Finally, the influence of joint size in the structural response during deployment is illustrated.