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7/14/2013 7:51 P.M. ET

Baker makes first Minor League rehab start

CHICAGO -- The Cubs' Scott Baker, rehabbing from Tommy John surgery on his right elbow, made his first Minor League start on Sunday, pitching three innings for Class A Kane County.

Baker gave up four runs on six hits and one walk while striking out two against West Michigan, and was lifted after 56 pitches. All of the runs came in the first inning, including two on a two-run homer.

Cubs manager Dale Sveum wasn't too concerned about Baker's numbers, but he was happy the right-hander was back on the mound for a game. Baker had the procedure on his elbow in April 2012.

"Right now for him, it's more about getting the work in and getting comfortable," Sveum said. "Today was a big hump to pitch against hitters and get in a real game and the whole atmosphere. Hopefully, we see a gradual pickup in the velocity and all that."

Baker was expected to make at least three more Minor League starts, and if all goes well, could join the Cubs in about a month.

Gillespie happy to have opportunity with Cubs

CHICAGO -- Cole Gillespie was happy to be reunited with his Oregon State teammate, Darwin Barney, on the Cubs.

Gillespie was added to the Cubs' active roster on Sunday, one day after being claimed off waivers from the Giants. To make room, the Cubs designated right-handed pitcher Henry Rodriguez for assignment.

Gillespie and Barney played on the OSU team that won the College World Series in 2006.

"We share a lot of great memories together, and it's pretty fun to be reunited at the big league level," Gillespie said.

The outfielder batted .277 in 74 games for Triple-A Fresno before being called up to the Giants on July 5. He went hitless in nine big league at-bats before he was designated for assignment on July 9. What kind of hitter is he?

"I'm a gap-to-gap guy, like to hit doubles, occasional pop," Gillespie said. "I feel I can steal some bases. I like to think I can do the little things good."

Gillespie was with Cubs manager Dale Sveum in the Brewers' Spring Training camp when Sveum was their hitting coach.

"It seemed like he's seen me more than I thought he has," Gillespie said.

The 29-year-old is just hoping for some regular at-bats. Gillespie will likely get starts against left-handed pitchers.

"It's been up and down the last few years, and hopefully, I get a pretty good opportunity here," he said.

Rodriguez, 26, had a 4.09 ERA in 22 relief appearances with the Nationals and Cubs this season. He was acquired from Washington on June 11.

Extra bases

• Outfielder David DeJesus will head to Arizona on Monday to begin what he hopes is an efficient week of rehab work at the Cubs' facility.

DeJesus, sidelined since June 14 with a sprained right shoulder -- sustained when he crashed into the outfield wall at Citi Field -- will work out in Mesa and play in Rookie League games. If all goes well, he could join the team on its road trip against the D-backs from July 22-25, or in San Francisco from July 26-28.

• Nate Schierholtz did not play for a second straight game Sunday, nursing numerous aches and pains. The outfielder ended the first half with a career-high in home runs (11). He has gotten all of the starts in right against right-handed pitchers. Sveum wasn't sure if they would have to give Schierholtz more time off in the second half.

"We'll see what happens when the break is over, to see where he's at," Sveum said.

• Right-hander Jake Arrieta, acquired from the Orioles in the Scott Feldman deal, struck out nine and gave up one run on three hits and one walk over six innings for Triple-A Iowa on Sunday. It was his third and longest start for the Minor League team.

• Sveum was headed to Las Vegas for the All-Star break to visit his daughter. Some of the players were going to take advantage of the time off and go home, while others were headed to Wisconsin water parks.

The coaches and Sveum have put in long hours.

"It's a 24/7 job, and some coaches take it home, and it gets a little worse," Sveum said. "There won't be any grinding [at the All-Star break]."

The Cubs leave Thursday for Denver, where they will kick off the second half with a 10-game road trip.

Carrie Muskat is a reporter for MLB.com. She writes a blog, Muskat Ramblings, and you can follow her on Twitter @CarrieMuskat. This story was not subject to the approval of Major League Baseball or its clubs.