Jürgen Hennicke challenged the designers of structural membranes stating that "Structural membranes, if not designed as such, require an imposing steel structure". Responding to this challenge, a comparative study has been launched to assess the impact on the design efficiency of considering or not the structural principles of membranes, that is: only tension, funicularity, curvature and pre-stress. In a previous paper the general approach of the research and the first results have been presented concerning rigid frames, I-beams, trusses, trussed arches, arches on branched masts, ETFE cushions, cable beams and flying masts. This paper shows more cases to complete the most usual repertoire including cable-stayed, castellated and void beams, grid shells, cable domes, ridges and valleys, textile halls, inflatable tubes, modular flying masts, tied ETFE cushions, modular photovoltaic ETFE cushions and pneumatic structures. The conclusions obtained during the previous research have been confirmed and completed. The lightest structures are those that avoid or reduce bending and the values obtained by varying the support structure vary significantly. The sag/span ratio affects the internal force. On the other hand, the ratios of surfaces and the weight of the membrane vary little. However attention has to be paid to deformations. In any case, what can really improve the efficiency of the structure is its conceptual approach. In the case of membrane structures, it is a matter of satisfying the basic principles of only tension, funicularity, curvature and pre-tension, avoiding bending. Resorting for example to flying masts, arches, beams and the interior columns disappear in exchange for the interior flying masts and the exterior cable-stayed masts subjected to simple compression. In addition, the methodology used and the values obtained can be applied to estimate and compare the efficiency of a design.