Last month, Lance Armstrong boarded a plane for Denver to do something several of his lawyers had advised against: sitting down for a private conversation with the head of the U.S. Anti-Doping Agency.

Travis Tygart had given the star cyclist no reason to believe that USADA would soften the lifetime ban from elite competition for what the agency called the "most sophisticated doping program on the planet." But Mr. Armstrong hoped he could change that.

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