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Mims then was selected by the Chargers 23rd overall in the first round of the 1992 NFL Draft. He played eight NFL seasons, seven with the Chargers and one with the Washington Redskins before retiring in 2000. Included in that span was a stretch of 46 consecutive games started during the 1994-96 seasons. Mims tallied 42 sacks for his career, including season highs of 11 in 1994 and 10 during his rookie campaign of 1992.