The White Sox have pushed Jake Peavy's next start from Sunday to next Tuesday against the Royals. The move will give Peavy extra time to build strength in his shoulder. The veteran right-hander expressed a lack of velocity and sharpness following his last start before the All-Star break, when he gave up five runs on 10 hits over 4 1/3 innings against the Twins. Phil Humber will move up to take his place Sunday against Detroit.