"We threw him in there after a real workload," said Cooper of Belisario. "Getting after it, two innings, an inning the next day, here's two innings. Then close for us.
"I think he entered that not at full strength. Now, I think the two days off, hoping that helped him get it back together."
Cooper views Thursday's team off-day as a way to give all of his pitchers an extra day. The White Sox have another day off one week from Thursday between road series against the Dodgers and Angels.
"Guys are throwing the ball well," said Cooper of the bullpen, which ranks among the American League leaders since April 26 in opponents' average (first, .195), ERA (second, 2.91) and innings pitched (fifth, 92 2/3). "The biggest thing on my mind with the bullpen is giving them some time to regroup a little bit."
Belisario tossed a 1-2-3 ninth inning, with one strikeout, for his third save in Tuesday night's 2-1 victory.
Scott Merkin is a reporter for MLB.com. Read his blog, Merk's Works, and follow him on Twitter @scottmerkin. This story was not subject to the approval of Major League Baseball or its clubs.