The constant-volume melting entropy of natural rubber (cis-1,4-polyisoprene = c-PIP) is small compared with other linear polymers. With the aim of understanding this behavior a reliable structural model for the crystalline state of c-PIP is needed. To this end the recent study by Takahashi and Kumano (T-K) has been revised, using the same X-ray diffraction measurements published by these authors. The new study has employed different refinement methods and considered several structural models. The chain structure claimed by Nyburg (S T (S) over bar cis (S) over bar T S cis) has been confirmed, but the resulting chain torsion angles are different, both if the glide-plane chain symmetry is assumed (R = 0.079) and if such chain symmetry is waived. (R = 0.067. The chain torsion angles for this model are 86, 171, and -88degrees, cis, and -120, -170, and 116degrees, cis.) At the chain packing level, while the disorder claimed by Nyburg and by T-K is not supported by the diffraction data, a different disordered model improves the F-c vs F-o fit giving a good crystal packing. Also the hypothesis of an orthorhombic structure (suggested in the past by Natta and Corradini) has been explored (R = 0.090). The implications of the crystalline structure and its possible conformational disorder on the low melting entropy are discussed.