A systematic study of the diluted lamellar phases of the OG/C(12)E(4) system with different alkanols has been carried out by small-angle X-ray scattering (SAXS). The measurements have been made as a function of both the concentration and the alcohol type. Several different form factor models have been used to estimate the differences in bilayer topology induced by the presence of alcohol. For the infinite lamellae form factor (with a high-low-high electronic density profile across the membrane), there is a good fitting of samples with a X(OG) = 0.1 ratios. Only the free parameters correspond to the pseudomolecule composition and hydration number, which resulted in two water molecules per ethylene oxide group in the polar head irrespective of the alkanol chain length and concentration. However, samples with higher OG content can be quite well fitted by a core-shell disk model. For the samples with higher OG content, we find the participation of OG in the disks to be important. From the line-shape analysis of SAXS data, the half-thickness of the hydrophobic layer and the thickness of the hydrophilic layer have also been obtained. The results suggest significant mixing of the surfactant acyl chains corresponding to both sides of the lamellae and the transition from vesicles to open bilayer fragments without macroscopic phase separation.