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Timothy Bradley gave Alexander his only loss in his career thus far. How nice would it be to avenge that loss? Bradley's next opponent is the pound-for-pound best in the world Manny Pacquiao (54-3-2, 38 KO).
Losing to Pacquiao is very possible and the best way to entice a fighter into giving a rematch to a loser is for the reluctant fighter to suffer a big loss.
Bradley won't want to go back to million-dollar paydays when he's expected to make $5 million against Pacquiao. A loss to Pacquiao would make him dart toward Alexander, if only for his WBC ranking.
Beating Alexander again would net Bradley a coveted potential mandatory challenger position opposite WBC champion Floyd Mayweather. Mayweather is the other big money-making fish in boxing.
Though Bradley's promoter Top Rank is often at odds with Mayweather as evidenced by the highly toxic Mayweather-Pacquiao negotiations, Mayweather-Bradley would be much easier to make.
Bradley would be willing to get in his place and accept a smaller purse and stringent drug testing to be back in the limelight. But first Bradley would have to get through Alexander.
Alexander was dominated the first time, but he wasn't beaten in such a way that he couldn't adjust to beat Bradley in fantastic fashion. He'll need a better game plan which will be hard, but quite doable.