BOSTON -- The names of Chris Sale, Jose Quintana, Jose Abreu, Avisail Garcia and now Carlos Rodon would be placed on the list of untouchables as far as players to potentially be moved by the White Sox in the upcoming non-waiver Trade Deadline period.

The only thing is the White Sox don't really work by the theory of absolute untouchables.

"Part of our responsibility is to stay in contact with clubs and find out how they value our players and see what opportunities there are for us to get better," White Sox general manager Rick Hahn said. "We don't hang up on anybody."

Of course, the White Sox would need a talent haul in return to almost literally knock the cell phone out of Hahn's hands to move any of the aforementioned players, so look for all of them to continue playing crucial roles in Chicago. But talk about one close-to-unmovable player might lead to talks moving on to something more attainable.

"A lot of times, you start off a conversation with them expressing interest in a player you may not be so inclined to move," Hahn said. "Based on their need, it leads to a different opportunity to make a deal that's a little more palatable. It doesn't make any sense to close off any conversation -- even if you know the odds are very long against anything happening on a certain player."

Cooper likes bullpen, but needs a closer

CWS@BOS: Belisario deflects ball, recovers for out

BOSTON -- Don Cooper likes his bullpen.

Of course, the fiercely loyal White Sox pitching coach is going to stand behind his charges through good times and bad. But he definitely likes the arms he has to work with -- when they are used in their originally designated spots.

"All of the guys are doing well in the jobs that they were expected to have: Sixth, seventh, eighth," Cooper said. "But the problem is we've yet to find a guy that can go out there on a consistent basis and get the last three outs, so to speak."

That problem became evident once again Wednesday night when Chris Sale was pulled from the game with two outs in the eighth, Dustin Pedroia at the plate and Mookie Betts on third with the White Sox leading, 4-0. Jake Petricka, who had thrown 11 straight scoreless innings and allowed just three hits over that stretch, was called in and couldn't retire any of the four batters faced. Javy Guerra bailed out Petricka in the eighth but couldn't hold the lead in the ninth.

The absences of Matt Lindstrom and Nate Jones due to injury have rearranged the bullpen alignment, as Cooper pointed out, and contributed to the relievers allowing four runs or more 14 times this season. The White Sox have a 2-12 record in those games, and according to Elias, the last four Major League Baseball games in which a team lost after taking a four-plus run lead into the eighth or later were all by the White Sox.

Those other three late White Sox losses were June 25 at Baltimore, June 7 in Anaheim and Sept. 21, 2013, at Comerica Park.

"With that being said, we still believe in them. They are our guys," Cooper said. "This is what we have and this is what we are going to go to war with. I'm OK with that. Each one is giving the best we got."

Ventura explains reasoning for pulling Sale

CWS@BOS: Sale strikes out six over 7 2/3 innings

BOSTON -- Chris Sale took a 5-0 shutout into the eighth inning at Angel Stadium on June 7, only to give up five runs in five batters, culminating with Mike Trout's game-tying grand slam. White Sox manager Robin Ventura was criticized for leaving Sale in the game too long.

On Wednesday night, Ventura pulled Sale at 107 pitches with the White Sox leading, 4-0, with two outs in the eighth and Mookie Betts on third base. The bullpen couldn't hold the lead, and once again Ventura was criticized -- only this time for taking out Sale too early.

Two different scenarios, but the same basic target of Ventura. It seems to be a natural progression when the bullpen struggles.

"You know what?" White Sox pitching coach Don Cooper said. "You are damned if you do and damned if you don't."

"That's just part of the job," said Ventura of the criticism. "But we're trying to find a way to get these guys in good situations and compete, all the learning stuff that goes with it. You want them to do well and you're trying to put them in spots that are the best fit for them."

Ventura added that his young guys will get used to pitching in these big spots, because this is the bullpen the White Sox have. But more of the pregame focus for Ventura's media session centered on the reasoning for pulling Sale at that point in his final first-half start.

Ventura's explanation was that if Sale was going to get Dustin Pedroia, who was the first batter faced by Jake Petricka, then Sale also was going to get left-handed-hitting David Ortiz. And the plan for the evening was 110 pitches for Sale, who both Ventura and catcher Tyler Flowers said wasn't quite as sharp as usual.

"We are going to take care of his health. Chris Sale is our crown jewel," Cooper said. "I remember when all hell was raised when he threw [127] pitches [against Boston on April 17]. With that being said, Chris Sale is a very, very good pitcher that if he keeps doing what he's doing, he's on the way to greatness.

"Chris did his job last night. We should be able to expect to get four more outs, and obviously those have been elusive outs for us."

Reliever Jones determined to pitch again in '14

BOSTON -- There are still no doubts in the mind of White Sox reliever Nate Jones that he will pitch again during the 2014 season.

"Absolutely. There's no thought that comes across my mind that it would have to wait until Spring Training or anything like that," Jones said. "I have confidence that it's going to be this year for sure."

Jones continues to travel with the team and rehab from a microdiscectomy performed on May 5. The hard-throwing right-hander basically follows the same daily procedure -- seeing how his body reacted from activities the day before, and if all is good, keep pushing forward. White Sox head athletic trainer Herm Schneider writes a note each day for Jones, and that's what he does in terms of running and throwing.

The distances of Jones' throws off flat ground vary from 90-150 feet.

"It has gone fairly well, fairly smooth," Jones said. "There will be some days when I would go out there and throw, because it's all new motions for my back after the procedure, and the next day maybe we wouldn't do as much. But there's not been any real setbacks or nothing like that.

"When we do new stuff, I still get a little sore in my hip. But that comes with the territory and is no big deal at all."

Third to first

Tyler Flowers wore glasses during Wednesday's contest against the Red Sox, but it was just a change of pace for the catcher, and not a sudden vision correction. Flowers usually wears contacts.

• Josh Phegley, the catcher for Triple-A Charlotte, has been added to the International League All-Star team. Phegley, 26, is hitting .253 with 13 homers and 38 RBIs for the Knights.

• Class A Winston-Salem manager Tommy Thompson has been named to the same position with the Melbourne Aces of the Australian Baseball League for the 2014-15 season. The ABL's season runs from Nov. 7, 2014 to Jan. 25, 2015.