But do they have enough in the bullpen?
One overlooked addition from the eventful Winter Meetings of two weeks ago was veteran LaTroy Hawkins, whom the Angels signed to a one-year, $3 million deal to likely serve as a right-handed setup option alongside lefty Scott Downs.
As general manager Jerry Dipoto said leading up to the move, "We're looking to complement [closer] Jordan Walden, not replace Jordan Walden."
The question is whether Dipoto has complemented Walden enough. More specifically, whether the addition of Hawkins -- who put up a 2.42 ERA in 52 appearances for the Brewers last year, but just turned 39 and will be heading into his 18th season -- is enough to vastly improve a bullpen that finished 2011 tied for the American League lead in blown saves.
Dipoto, at least, is still exploring his options.
And while it's highly unlikely that the Angels will become serious players for someone like Ryan Madson, there are still some affordable bullpen arms that can be had via free agency.
One interesting candidate is Joel Zumaya, who should come cheap, throws awfully hard and has experience in the back end of successful bullpens.
The Angels had scouts present during what was deemed to be a successful showcase by Zumaya last Wednesday, when the former Tigers reliever threw in front of an estimated 50 evaluators in Houston. One attendee told Ken Rosenthal of FOXSports.com and MLB Network that Zumaya threw his fastball from 93-96 mph, sported a decent curveball and had good command.
The 27-year-old right-hander missed all of last season after undergoing exploratory surgery on his throwing elbow in May, the latest in a myriad of arm troubles that caused him to average just 27 appearances through the four seasons that followed an impressive 2006 rookie year.
At this point, Zumaya may just be hoping for a big league contract.
The Angels have also been in touch with the representative for former reliever Darren Oliver, a source familiar with his thinking told MLB.com. Oliver's preference is still to return to the Rangers, but is "not ruling out other contending teams," the source said, adding that Oliver would even be willing to defer most of his salary to accommodate the money-tight Halos.
Oliver put up a 2.29 ERA in 61 appearances last year, but is 41 and would give the Angels three lefties in the bullpen -- along with Downs and Hisanori Takahashi.
Then there's Francisco Cordero, perhaps the best -- and most expensive -- free-agent reliever remaining after Madson.
Cordero's agent, Bean Stringfellow, told WEEI.com on Tuesday that the Angels are one of four teams in play for the right-hander's services, along with the Reds, Red Sox and a fourth, unidentified club.
But Cordero's asking price may be too high for the Angels, now that their 2012 payroll is expected to top $160 million with the Pujols and Wilson signings. Stringfellow told WEEI.com the three-time All-Star, who averaged 38 saves per season from 2004-11, is looking for a multiyear deal and is only interested in going into a situation where he's the clear-cut closer -- which, in Anaheim, would mean the young Walden is supplanted.
Behind Walden, the Angels have two solid lefties in Downs and Takahashi, along with the newly acquired Hawkins and a collection of relatively inexperienced righties -- seemingly Rich Thompson (3.00 ERA in 54 innings in 2011), Bobby Cassevah (2.72 ERA in 39 2/3 innings) and Trevor Bell (3.41 ERA in 34 1/3 innings).
Some other right-handed options in the free-agent bin include: Luis Ayala, Todd Coffey, Juan Cruz, Brad Lidge, Scott Linebrink, Mike MacDougal and Dan Wheeler, among others. Most of them may not sign deals until more materializes later in the offseason, and sources said the Angels have yet to reach out to Ayala or Wheeler in particular.
But the offseason is still relatively young -- and the Angels may not be finished addressing the 'pen just yet.
Alden Gonzalez is a reporter for MLB.com. Read his columns and his blog, listen to his podcast and follow him on Twitter. This story was not subject to the approval of Major League Baseball or its clubs.