About that second left-hander in the White Sox bullpen ...

Cory Luebke

The White Sox made their second round of spring cuts Wednesday afternoon.

Pitchers Chris Beck, Tyler Danish, Brad Goldberg and Giovanni Soto were optioned to Triple-A Charlotte, along with outfielder Willy Garcia. Catcher Alfredo Gonzalez was optioned to Double-A Birmingham. Pitchers Aaron Bummer and Blake Smith were reassigned to minor league camp.

We said at the start of camp that the Sox were looking for a second left-hander in their bullpen to complement Dan Jennings, and it looked as if Soto might be one of the top contenders -- if not the leading contender.

Turns out the Sox don't think that much of Soto. He's been optioned after making only two Cactus League appearances.

So, who is left in the mix for that other left-handed spot? Matt Purke hasn't allowed a run this spring over four appearances and 4.2 innings pitched. Brian Clark is getting an extended look -- he's appeared in seven games and fared reasonably well -- a 2.70 ERA in 6.2 innings. But, Clark has walked four, which is a bit of a red flag.

Jace Fry, who is coming back from Tommy John surgery, has worked in six games with a 4.15 ERA in 4.1 innings. But again, four walks -- that's a high total. A surprise contender has emerged in veteran reclamation project Cory Luebke. The 32-year-old has 1.35 ERA in five games and 6.2 innings pitched this spring.

Luebke has struck out five and walked two, and the big key for him is proving he has regained his control. Once upon a time, in 2011, Luebke was a big leaguer. He had a 3.29 ERA in 46 games (17 starts) for the San Diego Padres. But multiple Tommy John surgeries kept him out of the majors from 2013 to 2015.

He resurfaced with the Pittsburgh Pirates in 2016, and he was terrible -- a 9.35 ERA in nine games. He walked 11 in 8.2 innings. To make the Sox, he'll have to continue to avoid walks and show that he isn't susceptible to meltdown-style innings. Luebke has starting experience, so in theory, he could be the second left-hander *and* the long reliever.

Or perhaps the Sox will decide to go with only one left-hander and keep right-hander Michael Ynoa, who is out of options, on the roster.

Under that scenario, the Sox could use right-hander Zach Putnam is certain situations against tough left-handed hitters. Putnam's split-finger pitch tends to be tough on lefties, and when healthy in 2016, he held left-handed hitters to a .546 OPS. (Righties had a .694 OPS).

Knowing that Putnam is an option, perhaps it isn't essential the Sox keep a second left-handed reliever, if they decide they don't want to keep Luebke or give Purke another kick at the can.

White Sox avoid arbitration with Todd Frazier, Dan Jennings, Jake Petricka

Todd Frazier

The White Sox on Friday avoided arbitration with three players, agreeing to one-year contracts with third baseman Todd Frazier and relief pitchers Dan Jennings and Jake Petricka.

Frazier's deal is worth $12 million. He is coming off a season where he led the team in home runs (40) and stolen bases (15) despite a disappointing .225/.302/.464 slash line. He also ranked second on the Sox with 98 RBIs.

Coming into the offseason, Frazier, 30, was a good bet to be traded before Opening Day -- and maybe he still will be. However, there have been few rumors involving Frazier, and there still are several right-handed power-hitting free agents who remain unsigned (Mike Napoli, Mark Trumbo, Jose Bautista). Until those guys come off the market, there might not be much interest in Frazier -- especially since he is coming off a down season in terms of batting average.

He could eventually be traded for prospects as part of the rebuilding plan. Or maybe he won't be. Essentially, he's the Sox's third baseman until he's not. (How's that for insight?)

Jennings, 29, is coming off one of his better seasons -- a career-high 64 appearances with a 4-3 record and 2.08 ERA. His contract will pay him $1.4 million.

Petricka, 28, appeared in only nine games in 2016 before undergoing season-ending hip surgery. His deal is worth $825,000.

Although the Sox are rebuilding, they might enter the 2017 season with a bullpen that looks very similar to the one from last year. Closer David Robertson, set-up man Nate Jones, Jennings, Petricka and Zach Putnam all remain on the roster.

The only two guys gone from last season are Matt Albers, who was too ineffective to be retained, and Zach Duke, who was traded to the St. Louis Cardinals in July.

Right now, the projected bullpen includes the five guys listed above, plus Tommy Kahnle. After that, the Sox still need a second left-hander to go along with Jennings. As it stands, the next-best left-handed option in the organization is 25-year-old Giovanni Soto, a waiver pickup who last pitched in the big leagues with the Cleveland Indians in 2015.

Given that Robertson, Petricka and Putnam are all coming off surgery, we might not see too many changes in the bullpen this offseason -- just because the Sox need to hold onto as much veteran depth as possible to get through 2017. One thing a rebuilding team does not want is for prospects to be forced into big-league duty prematurely because of injuries to veteran stopgaps.