Rabbit psoas muscle fibres, relaxed and in rigor, have been freeze substituted for electron microscopy. Fourier transforms and average density maps of micrographs of transverse sections have been obtained and compared to X-ray diffraction data. The Fourier amplitudes from rigor and relaxed muscle are comparable to equatorial data from X-ray diffraction of muscle if there is more disorder in the electron micrographs which can be described by a 'temperature' factor. The phases of reflections out to the 3,2 have been determined; those reflections at the same radius and therefore not separable in the X-ray patterns, such as the 2,1 and the 1,2, are separated in the transforms of sections through the A band. In transforms from both rigor and relaxed muscle they have the same phase. In rigor muscle they have different amplitudes. All the phases are positive or negative showing that the lattice is centrosymmetric at the resolution obtained. The phases obtained generally support those suggested by model building studies using X-ray diffraction data. In rigor muscle, areas where the cross-bridges are regularly attached are clearly seen in thin transverse sections. A handedness to this structure is indicated by a lack of mirror symmetry, in both the Fourier transform of thick sections, and in the averaged density map. This correlates well with the arrangement where the myosin head is bound as in the acto-S1 structure but only to actin monomers within a limited azimuthal range.