FORT WORTH, Texas—Dallas Cowboys cornerback Adam “Pacman” Jones once again must earn his way back into the NFL, and it likely will take more than being on his best behavior.

The NFL suspended Jones for at least four games Tuesday for violating the league’s personal conduct policy. Commissioner Roger Goodell will determine the full length of the suspension after the Cowboys’ game in Washington on Nov. 16.

“If he earns his way to a point that he can be considered to play again, then I would support that,” Cowboys owner Jerry Jones said. “Frankly, just as he earned through...

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