DENVER -- In their quest to win a second World Series championship in four seasons, the Cubs bolstered their bullpen in a big way by signing All-Star closer Craig Kimbrel to a three-year, $43 million contract last Friday.

After throwing his first bullpen in a Cubs uniform Saturday at Wrigley Field, he threw another in Arizona on Monday as he works his way toward throwing live batting practice later this week.

"It's just like how Spring Training would go," manager Joe Maddon said. "Just go back and look at your Spring Training notes, it'll lay out pretty much the same. ... I'm not concerned. The guy's done it before, and I really rely, in this situation, on the player himself.

"[Pitching coach] Tommy [Hottovy] has laid it out with the medical people. You have to remain flexible with it both ways, either short or long. You just don't know yet, so let it play out. I'm not even thinking about it until it actually gets closer."

Hottovy said last week after Kimbrel's first bullpen session that his velocity, spin and overall stuff was "elite," and that he was "ahead of the game" when it came to getting himself ready after not having pitched in a game since Game 4 of the World Series.

Kimbrel, 31, is a seven-time All-Star with a career 1.91 ERA and 333 saves, most among active relievers. He struggled somewhat for the Red Sox in the postseason last year, posting a 5.91 ERA in nine outings for the World Series champions.

"I liked his accountability," Maddon said. "We've talked about the end of last season, and no excuses. He said this is how it was and he's got to do better. There was nothing to not like about [his introductory news conference]. ... There's a real strong thread of self-confidence there. He knows who he is. That's what I gathered."