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4/6/2014 1:35 P.M. ET

After first hit in Majors, Barnhart goes for seconds

NEW YORK -- Reds rookie catcher Tucker Barnhart notched his first big league hit with a third-inning single over second baseman Daniel Murphy that went into right field during Saturday's 6-3 loss to the Mets. Barnhart didn't wait long for hit No. 2, when he blooped a single over Murphy into short right field in the fifth.

While the ball from hit No. 2 wasn't saved, Barnhart does have possession of the first one.

"It's nice to get it out of the way and take a deep breath and just worry about getting more and getting more wins," Barnhart said.

Barnhart, who made the team after Devin Mesoraco went on the disabled list at the end of Spring Training, has made two starts and appeared in a third game as a defensive replacement. He was a battery mate with Homer Bailey on Wednesday and caught ace Johnny Cueto on Saturday. While Bailey struggled some, Bailey allowed two runs and five hits over seven innings.

"I'm getting to the point where I'm feeling pretty good," Barnhart said. "I thought that Johnny and I worked well together [Saturday]. Homer and I did the other day also. It's good to be out there getting my feet wet and getting to the point where it's all about playing baseball. It's not worrying about the nerves or anything like that."

There's a good chance Barnhart will be sent down to Triple-A Louisville this week, as Mesoraco is expected to rejoin the club in St. Louis on Monday. But manager Bryan Price has very positive reviews about the rookie's early performances.

"He's been terrific," Price said. "You don't set up high expectations for anyone that comes up, initially, as an offensive player -- especially as a catcher. You hope they defend well and work with the pitching staff. He's done a remarkable job with pitch selection, working with the starting pitchers and the bullpen.

"I think he's going to be an outstanding player, I really do. The two hits were a bonus. We didn't bring up here to hit .350. We brought him up here to catch and hold down the fort until Devin is ready and he has certainly done that. I have no apprehension to catch him and put him in the lineup."

Hamilton remains out with injured finger

NEW YORK -- Reds leadoff hitter and center fielder Billy Hamilton was given another day out of the lineup on Sunday because of a jammed left middle finger. But the prognosis was optimistic that Hamilton would not be out much longer.

"It's a lot better today," Hamilton said. "The swelling has gone down."

Chris Heisey led off and started in place of Hamilton for the series finale against the Mets.

Hamilton was a pinch-runner when he was injured trying to steal second base on a headfirst slide during Friday's 4-3 loss to the Mets. He was able to play defense in the ninth inning of Saturday's 6-3 loss.

"I didn't get a ball hit to me. But when I was catching and throwing, I could still feel it," Hamilton said. "I was able to squeeze the glove, enough if I had to make a play."

Hitting remains the primary issue at this point.

"It bothers me more batting right-handed than it does left-handed," Hamilton said. "If I had to bat yesterday, it would have been left-handed."

Reds manager Bryan Price felt that it was possible for Hamilton to be back in the lineup on Monday afternoon, when the team opens a three-game series at St. Louis.

"He's had great improvement overnight," Price said. "It's a day-to-day thing. We have to be confident he's comfortable swinging the bat and doing all of the things he needs to do."

Mesoraco, Broxton close to returning

NEW YORK -- Reds catcher Devin Mesoraco (strained left oblique) was 0-for-2 with a strikeout in his third and final rehab assignment game on a rainy Saturday for Double-A Pensacola.

"They took him out early after [five] innings because of the weather," Reds manager Bryan Price said. "They were a little bit concerned with him being so close to returning that he could be injured on the field, so they took him out."

Mesoraco could be activated on Monday from the disabled list. The Reds will be opening a three-game series vs. the Cardinals.

"It appears that he will meet us in St. Louis," Price said. "That's the protocol we originally established so I anticipate seeing him [Monday.]"

With Mesoraco catching, Reds reliever Jonathan Broxton (right forearm) started for Pensacola the second day in a row. Broxton threw one perfect inning on 14 pitches.

"It went fine. We anticipate that he's in good health," Price said.

Broxton is also expected to rejoin the Reds at St. Louis.

Worth noting

• Following Broxton on Saturday was the Reds' No. 1 prospect, right-handed pitcher Robert Stephenson. In only five innings, Stephenson struck out a career-high 11 batters with one hit and one walk.

Mark Sheldon is a reporter for MLB.com. Read his blog, Mark My Word, and follow him on Twitter @m_sheldon. This story was not subject to the approval of Major League Baseball or its clubs.