A novel technique of direct neutron-multiplicity sorting with a flat-efficiency detector is proposed to resolve the long-standing discrepancy between the Livermore and Saclay data of partial photoneutron cross sections. A flat-response neutron detector with the detection efficiency of 36.5±1.6% over a neutron energy range 0.01–5.0 MeV was developed by optimizing triple-ring configurations of He proportional counters embedded in a polyethylene moderator. The technique forms a foundation of measuring cross sections with x=1−3 for the photonuclear data project of the International Atomic Energy Agency. The methodology of direct neutron-multiplicity sorting and key experimental elements are presented.