Complicating matters is the fact that Yates, Boyer and Chris Resop are all out of options and there might only be room for two of them to begin the season in the bullpen.
"You don't want to lose guys like that and it looks like we might have to," Cox said, conceding he understands he likely won't be able to carry all three right-handed relievers on his Opening Day roster.
After Yates issued two walks during a scoreless eighth inning against the Indians on Wednesday, Cox quickly pointed out that he was impressed with the right-hander's ability to locate his fastball down in the strike zone.
Again on Thursday morning, without any provocation, Cox praised the effort provided by Yates, who has allowed two earned runs and issued five walks in 4 2/3 Grapefruit League innings.
"That's the best I've ever seen Yatesy," Cox said. "He's not going to give up nothing if he keeps everything down there."
Currently, the only four pitchers who are seemingly locks to begin the season as part of the seven-man bullpen are closer Rafael Soriano, Peter Moylan, Manny Acosta and left-hander Will Ohman. At the same time, Yates, who is attempting to develop a split-finger fastball, seems to be a favorite to win one of the remaining spots.
If Yates is on the Opening Day roster, Cox may have to decide between Boyer, who hasn't allowed a run in eight Grapefruit League innings, and Resop, who hasn't allowed a run in three of his four appearances.
With his fastball consistently flirting with 100 mph, Resop seems to have overcome the elbow problems that sidelined him with the Angels midway through last season. But to enhance his resume and chances of sticking in the Majors, the 25-year-old right-hander, who wasn't converted into a pitcher until 2003, will have to show more consistency with his secondary pitches.
While posting a 3.11 ERA in 43 appearances for Atlanta in 2005, Boyer, who didn't pitch regularly in high school, was more of a thrower than a pitcher. But the 26-year-old right-hander believes things have changed since he encountered the shoulder problems that forced him to miss most of 2006 and spend most of last season in the Minors.
"One of the biggest blessings of my pitching career so far might have been to be in Richmond last year as a starter to get those innings," Boyer said. "It let me really get a feel for my curveball and, man, it's really feeling good. I'm not just a one-dimensional pitcher anymore. I've got three pitches that the batter really has to worry about."
If he has to make a choice between Boyer and Resop, Cox's final choice for the bullpen will depend on whether he wants to carry a second left-hander or somebody who could provide some long-relief innings and, more importantly, occasionally serve as a spot starter.
Among the left-handers battling for a final spot, Royce Ring, who is also out of options, hasn't impressed and Jeff Ridgway took a step back by hitting consecutive batters before issuing consecutive walks during Thursday's eighth inning.
"Sometimes it takes [mistakes] to make the team or not and they do a little more than they should," Cox said in reference to the erratic outing endured by Ridgway, who had issued just one walk in his previous four innings.
The most surprising left-handed relief candidate is Francisley Bueno, who, despite issuing four walks in 10 innings, has received regular praise from Cox.
"I'll tell you who is good is Bueno," Cox said. "I know he walked a guy the other night, but he throws strikes."
Instead of carrying a second left-hander, Cox may opt to put Buddy Carlyle or Jeff Bennett in the bullpen. Despite allowing three solo homers on Wednesday night, Carlyle still received some praise from Cox, who thought the right-hander simply missed with a few pitches he might not have thrown during a regular-season game.
As for Bennett, who battled a bad sinus infection earlier in camp, he enhanced his chances of winning a roster spot with two scoreless innings on Thursday.