The issue of multiple equilibrium phases in compositionally heterogeneous random copolymers has been addressed by a series of small-angle neutron scattering (SANS) experiments. An ethylene−hexene (EH) copolymer, representative of many linear low-density polyethylenes (LLDPE) has been shown to contain a dispersed minority phase (volume fraction, φ ∼ 0.02) consisting of highly branched, amorphous material. The dispersed phase is eliminated to a good approximation by xylene extraction, which removes the low molecular weight and highly branched molecules. The extracted material contains a much higher fraction of branched molecules and hence has a greater proportion of the dispersed phase (φ ∼ 0.2). These findings support the prediction of liquid−liquid phase separation for compositionally polydisperse LLDPEs, whereby the more highly branched molecules in the distribution may phase segregate, even if the overall branch content is low.