Kershaw (shoulder) threw 4.1 innings in his rehab start with Triple-A Oklahoma City on Thursday, allowing two runs on six hits while striking out six and walking two while throwing 61 pitches, Ken Gurnick of MLB.com reports.

Kershaw got off to a shaky start, allowing a home run and walking two against the first five batters he faced, but he was able to limit the damage to two earned, and hit the 60-pitch benchmark the team had set for him in his first rehab appearance. Manager Dave Roberts said Wednesday that he was leaning toward having Kershaw make one more start for Oklahoma City as he works his way toward rejoining the big club.