This paper focuses on the magnetization characteristics of technicalNb3Al conductors, in particular the minimization of their hysteresis loss and low-field instability. Unlike the caseof Nb3Sn wirefabrication, the Nb3Al wire is fabricated by a phase transformation process, in which it is believed that theJc properties ofthe transformed Nb3Al phase do not depend on the filament size or shape, but rather are principally controlled bythe rapid heating and quenching or transformation conditions. However, the rapid heatingand quenching process forces us to use high-melting-point metals like niobium as thematrix. The use of Nb strongly affects the magnetization because of its superconductivityin low fields. In this paper, the magnetization properties of several kinds of technicalNb3Al conductors, including Ta matrix wires, were studied. The use of Ta was effective insuppressing low-field instability. In addition, we propose a new process to further minimizethe filament diameter by a re-stacking (RS) method, whereby the rapidly quenched strandsare re-stacked into a stabilizing material tube and co-drawn. This process leadsto a very fine multifilamentary structure with a filament diameter of less than15 µm, thereby substantially reducing the magnetization, as compared with high-performanceNb3Sn wires, e.g.RRP Nb3Sn wire. The ± 3 T hysteresis loss ofthe RS Nb3Al conductor was370 mJ cm−3 and the non-CuJc (12 T, 4.2 K) of theconductor was 1350 A mm−2. These values meet the ITER strand specification.