Challenge for A Great Persuader

A year ago, the star of James A. (for Addison) Baker III was at its zenith. Standing at Ronald Reagan's side in Tokyo, the 67th U.S. Treasury Secretary helped forge an agreement at the annual summit meeting for improved international economic cooperation. While Baker was accomplishing that feat, his aides in Washington were midwifing a tax bill in the U.S. Senate that became the basis for the most dramatic tax reform in more than 30 years.

Now the low-key, University of Texas-educated lawyer is facing some of his greatest challenges since he became Treasury Secretary in 1985. Baker, 57, is seeing...