A small-angle X-ray scattering (SAXS) study was conducted on melt-crystallized long-chain n-alkanes C162H326, C194H390 and C246H494. The main objective was to clarify the structure of lamellar crystals with the layer period a non-integer fraction (NIF) of the period of extended-chain crystals; the NIF form is the product of primary chain-folded melt crystallization (Ungar, G. and Keller, A., Polymer, 1986, 27, 1835) and it transforms subsequently to one of the integer folded forms. The extended-chain form crystallized from melt was also studied. Electron density profiles along the layer normal were reconstructed by inverse Fourier transformation using discrete diffraction intensities. The profiles were compared with the data computed from models. The best fitting models consist of alternating high- and low-density layers with relatively sharp boundaries. The high-density layers, representing the crystalline regions, have thicknesses which closely match either the calculated thickness of extended-chain layers with 35 degrees chain tilt (for the extended-chain form) or half that value (for the NIF form). In the extended-chain form a low density intercrystalline layer is observed with thickness between 1 and 3 nm, depending on chain length and temperature. In contrast, the non-crystalline layer in the NIF form is 6 to 8 nm thick. It has constant density and is truly amorphous, as indicated by the close match between SAXS and DSC crystallinities, which are less than two thirds for the as-formed NIF structure. While less than half the chains are folded in the latter structure, those that are have a fold in the middle (＇integer folding＇). Non-folded chains traverse the crystal layer only once, while their uncrystallized ends (cilia) comprise the amorphous layer. Within the crystalline layer of the NIF form chains are tilted at 35 degrees. The fraction of folded, fully crystallized chains increases with decreasing temperature at the expense of the amorphous layer, resulting in a reduction in amorphous layer thickness and overall lamellar periodicity (lamellar ＇thinning＇).