DeSclafani threw 40 pitches in the mound session, his second one since being shut down following a setback in what was expected to be his final rehab assignment start late last month. He also threw on Saturday in Philadelphia.
The throwing session was broken up into 20-pitch "innings" with a five-minute break in between. It was done as a way to further test the oblique.
"I think what it was before was the ups and downs [that caused the setback]," DeSclafani said. "I'd get hot and cool down, get hot again and cool down. By the time the fifth inning comes, you've warmed up and cooled down so much that it starts getting irritated."
The club will reassess its plan for DeSclafani when it returns to Cincinnati on Wednesday. He could have another bullpen session, a live batting-practice session or possibly try another rehab assignment.
"We're just trying to make sure we cover all our bases, actually re-cover all of our bases, since we've been down this road once before," Reds manager Bryan Price said. "This has been extremely smooth sailing since we re-initiated the throwing program. He hasn't had any setbacks or indicators that there could be a setback. We're back to being optimistic again that we could see him here pretty soon."
• Pitcher Jon Moscot (left shoulder irritation) is scheduled to have his second rehab assignment start for Triple-A Louisville on Friday. Moscot threw 69 pitches over five innings for Louisville on Sunday.
• Third-base coach Billy Hatcher was back with the Reds on Tuesday after he missed a game to attend his daughter's graduation. Jim Riggleman filled in for Hatcher on Monday after he served as acting manager on Friday in Philadelphia while Price served a one-game suspension.
• Next door at Quicken Loans Arena on Tuesday was Game 1 of the NBA Eastern Conference finals between the Cleveland Cavaliers and Toronto Raptors. A Toronto resident and Raptors season ticket holder, Reds first baseman Joey Votto said he was "totally geeked" for his team.
"I watched them from the first tip-off 20 years ago and all the guys -- Damon Stoudamire, Anthony Davis and all the players," Votto said. "Here they are now with a legitimate shot at going to the Finals. I'm totally excited for it."
Mark Sheldon has covered the Reds for MLB.com since 2006, and previously covered the Twins from 2001-05. Read his blog, Mark My Word, follow him on Twitter @m_sheldon and Facebook and listen to his podcast. This story was not subject to the approval of Major League Baseball or its clubs.