Phase behavior and small-angle neutron scattering (SANS) measurements are reported for poly(ethylene-co-20.2 mol % 1-butene) (PEB10) dissolved in supercritical dimethyl ether (DME). The phase boundary is located at pressures near 600 bar at 130 degreesC, and it exhibits a minimum in temperature near 105 degreesC where the cloud-point pressure rises sharply. Neutron scattering is performed with a high-pressure scattering cell designed for a large incident beam diameter, good mixing, and real-time viewing of the solution to ensure single-phase operation. The SANS results suggest significant variations in intramolecular correlations exist at length scales proportional to a few monomer units although the radius of gyration remains close to the unperturbed value at pressures from the cloud point to as high as 2400 bar. As expected, the intermolecular correlation length grows rapidly on approach to the phase boundary. The phase behavior and SANS data suggest that DME is very poor quality solvent even at high solvent densities.