The structure of a self-assembling system, bicopper ethyl-2-hexanoate, producing filaments in organic solvents, has been studied as a function of temperature, of solvent type, and in polymer solutions. While the rheological behavior in organic solvents can be accounted for by Cates' theory, the neutron scattering data rather suggest a two-population system: very long filaments and short filaments. Raising temperature or increasing polymer fraction both seem to promote the appearance of a significant fraction of individual bicopper complex molecules. These findings are discussed by considering side-by-side aggregation of short filaments.