Cleavinger (oblique) began a rehab assignment with Triple-A Oklahoma City on Saturday, per Eric Stephen of SBNation.com.
Cleavinger is currently on the 60-day IL, so he isn't eligible to return to the big club this season. That said, he is clearly progressing from his oblique injury given his ability to pitch in minor-league games. In two rehab outings, he has given up two runs (one earned) while striking out four batters over 1.2 innings.