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Research and development of copper stabilized Nb3Al strands and cables for a high field Nb3Al common coil magnet is ongoing with the cooperation of KEK-NIMS-Fermilab. In this work, newly designed K1 and K2 strands and cables were fabricated. The Kl strand used tantalum for the inter-filament matrix only and the K2 strand used it for the entire strand matrix. Wire breakage happened on the drawing of both precursors, and it may be caused by the de-bonding of the inter-filament as well as poorer cold-workability of the tantalum itself. Non Cu Jc's at 12 T were 1,300 A/mm2 at 4.2 K and 1,600 A/mm2 at 1.9 K, an increase of about 20%. The low field magnetic instabilities at 4.2 K could be suppressed with K1 and K2 strands because of the tantalum inter-filament matrix. Similar superconducting characteristics were obtained on K1 and K2 strands. However, K2 strands showed excessive separation of the copper stabilizer when made into Rutherford cables, although Kl strands did not. The copper stabilizer prefers niobium as an interface material to obtain good bonding.