The Cowboys, who have been searching for help at defensive tackle since training camp, gave the Raiders a conditional 2006 draft pick for Cooper.
Cooper will be inactive for today's game against Minnesota.
Interestingly enough, the Cowboys will head into Sunday's season opener at Minnesota with three rookie cornerbacks in Jacques Reeves, Bruce Thornton and Nate Jones backing up starters Pete Hunter and Terence Newman.
Powell was competing for the starting cornerback spot vacated by Mario Edwards throughout most of camp, but eventually lost out to Pete Hunter.
Cowboys Cut Powell; Trade for DT
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