A pressure vessel for neutron inelastic scattering experiments at 3000 atm maximum pressure is described. Rather thin walls with good neutron transmission properties are obtained by making the vessel of five cylinders, each of a high strength aluminum alloy, which are shrunk one upon another. This ``compound cylinder'' has a total wall thickness of only 13.5 mm for a (cylindrical) sample volume of 30.6 mm diameter and 65 mm length. The whole range 2π of scattering angles is accessible. Certain relations are given which were used in calculating optimal cylinder dimensions. Experiments with a lead single crystal show a reduction of Bragg peak intensity to 76% if the crystal is mounted in the vessel. A typical measurement at 3000 atm gives an increase of 2% in phonon energy.