BALTIMORE -- The Pirates agreed to terms with supplemental pick Barrett Barnes and signed third-round Draft selection Jonathan Sandfort on Thursday, marking the 10th and 11th prospects the team has locked up from this year's Draft class.

Barnes, an outfielder from Texas Tech who hit .325 with nine home runs and 49 RBIs last season, was the 45th overall pick.

Barnes left Houston on Thursday afternoon with plans to undergo a physical and officially sign on Friday.

Sandfort, a right-handed pitcher from Winter Springs High School in Florida, has been assigned to the Gulf Coast League Pirates. He was 8-1 with a 0.92 ERA and 72 strikeouts in 68 2/3 innings last season.

"The Pirates are excited to add the athletic and physical presence Jon Sandfort brings to the baseball field," Pirates director of amateur scouting Joe DelliCarri said in a release. "He possesses many positive traits needed to excel at pitching for a long time."

Karstens nearing his second rehab stint

BALTIMORE -- Right-hander Jeff Karstens threw a bullpen session on Thursday and is expected to begin his second rehab assignment on Tuesday with Double-A Altoona.

Karstens has been on the 15-day disabled list since April 18 with right shoulder inflammation and was scheduled to be activated this week before tweaking his hip flexor during a rehab start on June 7.

"Everything is checked off the list for today," Karstens said on Thursday. "Just looking to come back healthy. I'm tired of being hurt. I'm not paid to be hurt, I'm paid to pitch. And I feel like I'm not doing that right now."

Manager Clint Hurdle said Karstens threw 15 pitches, all fastballs, during Thursday's session.

If Karstens feels well on Friday, he will throw all of his pitches in a 35-pitch bullpen session on Saturday. That would set him up for a Tuesday rehab assignment, from which point he would have 30 days to return to the active roster under Major League Baseball rules.

With the news that Charlie Morton underwent Tommy John surgery on Thursday, Karstens is feeling a greater sense of urgency to return to a starting rotation that has been struggling on the back end.

"I'd be lying if I said there wasn't, but at the same time I have to make sure that I get back to pitching the way I can," Karstens said. "I'm in a good place right now, and hopefully all goes well and I'll be back soon."

Hurdle showing faith in struggling Alvarez

BALTIMORE -- Manager Clint Hurdle is committed to third baseman Pedro Alvarez. All he's asking for is a commitment in return.

Alvarez has been struggling all season, entering Thursday's series finale with a .191 average and just three hits in his last 35 at-bats. But Hurdle is set on keeping Alvarez in the Majors for the time being, as long as the third baseman settles on a consistent approach at the plate.

"There's a pretty good chance a player like Pedro, you send him down, he's going to do fine at Triple-A," Hurdle said. "I think this is a guy that we've made an investment in, that we've got to make a commitment to. If I'm going to ask him to make a commitment at the plate, I think there's got to be a commitment on my part as well."

Alvarez was in the Pirates' lineup on Thursday, as he started at third base and batted sixth.

Hurdle wants Alvarez to approach every at-bat the same way rather than make adjustments with every out. Constant change makes it difficult for a hitter to settle in and find success at the plate, according to Hurdle.

"You've got to give it some time," Hurdle said.

Hurdle has consistently encouraged Alvarez to keep swinging without worrying about his 65 strikeouts through 178 at-bats this season.

"A swinging bat is a dangerous bat," Hurdle said. "You're going to live with strikeouts. It's not as big a deal as it used to be. That's something I had to get over as a hitting coach. When I played, I had coaches say they'd rather give up a small body part than strike out. It's not the same way anymore."

Hurdle praised Alvarez's ability to keep his struggles at the plate from bleeding into his fielding and baserunning, saying that Alvarez gets secondary leads as well as anyone on the team.

"There's no moping or brooding when he gets on base, ever," Hurdle said. "He's dealing with this very professional, the challenges that he's having. That also gives you optimism that he's pushing. He's pushing and he's giving it everything he's got to work through this."

Worth noting

• Entering Thursday's action, Alex Presley, Garrett Jones, Jose Tabata and Casey McGehee were all hitting better than .300 in June after entering the month with averages at or below the .232 mark.

• Right-hander Daniel McCutchen, who has been on the disabled list since May 13 with a strained left oblique, began his rehab assignment on Thursday with Class A Bradenton.