Jake Peavy (rib) threw a bullpen session Tuesday. It wasn't a full effort session, but it's nonetheless the first time he's been on a mound since fracturing a rib. White Sox pitching coach Don Cooper said afterwards that the session was "better than I thought it was going to be." Peavy is slated for another bullpen session on Friday. The Palehose are hoping to get him back around the All-Star break.