The Yankees are expected to recall right-hander David Robertson to replace Bruney on Tuesday.
"It's not really fair to the bullpen, to Joe, to the team," Bruney said. "We have enough arms here where I don't need to be sitting here one day, able to pitch, and the next day not."
With no signs of structural damage in both Thursday's MRI and Friday's arthogram, Bruney said that he should not have to pitch with pain and looked forward to seeing a nerve specialist in New York to get a better understanding of what might be going on.
While Bruney's initial injury -- a right flexor muscle strain in his elbow -- was quantifiable, doctors have been unable to diagnose any lingering problems. What Bruney does know is that the pain doesn't go away, but it slightly lessens with each pitch.
"I don't think there's anything serious going on," Bruney said. "I think that possibly my nerve is a little irritated. I'm not a doctor, but everything structurally looks good. I'm still throwing 95, 96 [mph]. To me, there's got to be a reason why it hurts."
After tossing one inning following his reactivation, Bruney reported pain to Yankees manager Joe Girardi before last Thursday's game. Bruney said Monday that he also felt discomfort during his one inning of rehab work at Triple-A but believed he could pitch through it.
Bruney is 2-0 with a 3.00 ERA in nine games for the Yankees this season, serving as Mariano Rivera's primary setup man when healthy.
In Bruney's absence, Girardi said that the Yankees have seen good things from contributors like Alfredo Aceves, Phil Coke, Brett Tomko and Jose Veras, who could help soften the blow of losing Bruney again.
"We've had some guys that have had some success the last couple of weeks in his absence, so I don't feel that it's square one, in a sense," Girardi said. "It is a setback, and it's something we have to deal with. It's something we wish we didn't have to deal with."