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We are planning to demonstrate a quadrupole magnet with magnetic mirror structure by using 0.7-mm Nb3Al strands. As feasibility studies for this program, we investigated an influence of the diameter reduction of Cu-stabilized Nb3Al strands from 1.0 to 0.7 mm. Wire breakages and Cu separations did not happen with applying the cold die-drawing. The non-Cu Jc and n-values of the 0.7 mm strands did not degrade and could keep the same performance of the 1.0 mm strands. Although irregular deformations of Nb-Al filaments slightly occurred, magnetization properties of the 0.7 mm strands are almost the same as those of the 1.0 mm strands. Ta interfilament matrix of the 0.7 mm strands was also effective to improve the low field instability at 4.2 K. In addition, 27 strands Rutherford cable has been made by using the 0.7 mm F1 strand without any troubles. All of 27 extracted strands taken from the F1 cable showed very uniform Ic performance at 4.2 K.