PHOENIX -- Remaining healthy was one of the few things Jordan Norberto couldn't do in 2012. Otherwise, he was fantastic out of the bullpen for the A's.

So imagine Norberto's curiosity surrounding his potential for the 2013 campaign with injury issues -- specifically shoulder problems -- no more.

"I think I can do a lot for this team," Norberto said.

Manager Bob Melvin's not going to argue, not after he watched the 26-year-old southpaw succeed in many situations last year while compiling a 2.77 ERA and holding opposition to a .200 batting average spanning 39 games in a season shortened by two disabled list stints.

It's also for that reason Melvin wants to keep close watch on Norberto this spring, despite the lefty's insistence on remaining on the same schedule as his teammates.

"I'm more cautious of him than he probably wants me to be," Melvin said. "He wants to be a full-go guy, but he's so important to us, and we have such a long spring that we just want to make sure that each and every day he's healthy. You look what he did for us last year, and he was terrific in pitching in numerous types of roles. He's a valuable piece."

Norberto blended right in on Wednesday, when he threw his fifth bullpen session since December but first in front of A's personnel, tallying 26 pitches.

"I felt good," he said. "After my first and second bullpens, my shoulder felt tight, but since my third one, I've felt very good -- back to normal."

That's good news, considering he'll need all the time he can get in front of A's coaches this spring, with a flock of relievers vying for only a few bullpen spots.

"I don't want to be behind," Norberto said. "There's way too much competition for that."

Rooting him on back in North Carolina are his two daughters and wife, Jennifer, who is expecting the couple's third child, a boy, at the end of March.

Worth noting

• Newcomer Hideki Okajima made a strong first impression with his new team on Wednesday, just one day after agreeing to a Minor League deal. The A's lefty threw his first bullpen session, with Bob Melvin watching on.

"He did bounce some balls, but I tell you what, there's a lot of deception, a lot of downhill plane from his angle, and you pick up the ball late," the manager said. "It was nice to see him on the mound -- a lot of things that catch your eye."

• Right-hander Jarrod Parker also "looked great" in his first bullpen session of the spring, according to Melvin.

"You can tell he's gained a lot of confidence," Melvin said. "You could just see it. He's just a guy that belongs now."

Parker, who figures to slot into the No. 2 rotation spot behind only Brett Anderson following a tremendous rookie campaign, didn't even make the team out of camp last year.