"Jake Peavy was only half-kidding Friday about making the Class AAA all-star team.

The right-hander knows he'll have to make at least one more rehab start with Class AAA Charlotte before he can resume pitching for the White Sox after his strained right groin heals. That decision comes from Sox general manager Ken Williams.

''I begged to get out of a Charlotte trip,'' said Peavy, who has been out since Sunday, when he suffered the injury. ''But Kenny said, 'You won't go at the same speed in a bullpen session as you would in a game. I want you to have to cover first. I want you to exert the same energy at Charlotte before I activate you.' ­Kenny's the boss.''

Peavy already pitched for Charlotte twice this spring, as well as for Class AA Birmingham, while preparing to return from surgery last season to repair a torn latissimus dorsi muscle. He rejoined the Sox on May 11 and made five starts before having to leave Sunday's game against the Detroit Tigers after four innings. He's eligible to return June 21 at the earliest, but the timetable will be clearer after Monday, when he undergoes another MRI exam on the groin. "