To suppress the low-magnetic-field instability (flux jumps in low magnetic fields) of a rapid-heating, quenching and transformation (RHQT) processed Nb 3 Al superconductor, we had previously modified the cross-sectional design of an RHQT Nb 3 Al by adopting a Ta filament-barrier structure. Unlike Nb barriers, Ta barriers are not superconducting in magnetic fields at 4.2 K so that they electromagnetically decouple filaments. However, small flux jumps still occurred at 1.8 K, which is a typical operating temperature for the magnets used in high-energy particle accelerators. Furthermore, poor bonding at the Ta/Ta interface between neighboring Ta-coated jelly-roll (JR) filaments frequently caused precursor wires to break during drawing. To overcome these problems, we fabricated a new RHQT Nb 3 Al wire with a Ta/Cu/Ta three-layer filament-barrier structure for which an internal stabilization technique (Cu rods encased in Ta are dispersed in the wire cross section) was extended. Removing the Ta/Ta interface in the interfilamentary barrier (JR filament/Ta/Cu/Ta/JR filament) allowed precursor wires to be drawn without breaking. Furthermore, the Cu filament barrier electromagnetically decoupled filaments to suppress flux jumps at 1.8 K. The ductile Cu layer also improved the bending strain tolerance of RHQT Nb 3 Al.