The rupee has made a significant and swift comeback to hit a one-month high in a reversal from repeated all-time lows when it breached 80 per dollar for the first time ever. On Tuesday, the Indian currency hit a one-month high, strengthening for the fourth straight session, and was last changing hands below the 79 per dollar mark. The range of the rupee's moves also was below the 79-to-a-dollar mark for the first time since early July.