Peavy, who played for the U.S. in 2006 and 2009, said he was asked by the White Sox not to participate this time because of the wear and tear on his surgically repaired right shoulder.
"It was something I dearly loved doing," Peavy told MLB.com after the White Sox worked out on Tuesday at Camelback Ranch. "It was something I was very interested in and wanted to do again in 2013. I understand the experience and this is the last time I may be in uniform when it happens. It was a tough decision. I'm sad that I'm not going to be in it."
Dunn, who played for manager Davey Johnson in 2009, said he wanted to spend this spring getting ready for the season rather than participate in the tournament.
"It was a lot of fun," Dunn said. "But I knew there was a lot I needed to work on this spring. It's an extended spring and I want to make sure I'm ready for Opening Day. Any extra weeks I can get with the hitting coach fine-tuning some things, that's what I wanted to do."
The Classic, like the Olympics and soccer's World Cup, now comes around every four years. Dunn, 33 and a 12-year veteran, and Peavy, 31 and going into his 12th big league season, could be on the outskirts of -- if not done -- with their respective careers when the Classic returns in 2017.
That's why Peavy was geared up to play when he received calls from manager Joe Torre and pitching coach Greg Maddux a couple of months ago to judge his interest. Torre personally called every prospective Team USA player to gauge enthusiasm and commitment. He had Maddux, a 355-game winner and certain Hall of Famer next year when his name goes on the ballot, follow up with each of the pitchers.
Maddux played with Peavy on the Padres in 2007. And Peavy has never been shy about saying that it was no coincidence he had the best season of his career with Maddux as his daily mentor. Peavy won the National League's Cy Young Award and pitching Triple Crown that season with 19 wins, a 2.54 ERA and 240 strikeouts.
So one can only imagine Peavy's enthusiasm level when he was recruited for Team USA this year by these two men only months after re-signing with the White Sox for two years at $29 million with a $15 million option for 2015.
"Yeah, I heard from Joe and Greg Maddux, obviously the friend that he is," Peavy said. "I told Maddux that I would get ready and do it. Obviously, I understand the hesitation from the White Sox's standpoint. I had just gotten back last year into a form of being who I'm supposed to be. When [new general manager] Rick Hahn talked to me and said, 'Look, I'm going to object to this,' at the end of the day, you've got to be respectful to your authority and I didn't give any resistance. I sadly had to decline the opportunity, but it wasn't easy."
Torre ran into the same problem from the Yankees regarding Andy Pettitte, who pitched for Torre when he managed the Yankees, winning four World Series titles along the way. Pettitte told Torre and Maddux that, at 40, he wanted to play. But Yankees management also objected because the left-hander missed almost three months of the 2012 season with a broken fibula in his left leg. Torre didn't want to press it and Pettitte declined.
Blue Jays knuckleballer R.A. Dickey, Giants right-hander Ryan Vogelsong, Rangers left-hander Derek Holland and late additions Gio Gonzalez and Detwiler of the Nationals are the projected Team USA starters.
In contrast, Dunn made it known that he wasn't interested in playing this spring. Thus, he wasn't even on Torre's list. Dunn had one of his worst seasons in 2011 after signing with the White Sox as a free agent, missing 40 games largely because of an appendectomy.
"I just tried to come back from that surgery too quick," said Dunn, who batted .159 with 11 homers and 42 RBIs that season.
Last year, Dunn rebounded with 41 homers and 96 RBIs. However, he hit only .204, well below his .240 career batting average, so there certainly are areas of his game to work on this spring.
"Obviously [Team USA] didn't have to ask," Dunn said. "I made it known through certain people I was not really interested in doing it again this year just from the pure fact that I need to work here as opposed to going out there.
"But I loved it. It was a great event. It was a lot of fun."