Arizona has not decided when or where the 21-year-old will began a rehab assignment. Manager A.J. Hinch speculated that Upton, on the 15-day disabled list since Aug. 6, would be ready to head to the Minors sometime early next week.
Upton spent the past couple of days using a tee and hitting soft tosses. On Wednesday, he took swings in the cage with a coach pitching.
"Everything's going well. I'm feeling a lot better," said Upton, who was hitting .301 with 20 homers and 66 RBIs when he got hurt trying to steal second. "I'd definitely shut it down if I was feeling it. Right now, I'm getting [no pain] when I swing. So I think I'm almost there."
But Hinch is concerned less about Upton's offense than about other aspects of his game. Whereas an injured left oblique might affect a right-handed hitter's swing, Upton's strained right oblique is more likely to plague him while running on the basepaths or in the outfield.
So before giving him game action, Arizona will make sure that he is comfortable swinging and sprinting. Upton ran arcs -- tracing the infield's shape -- on the outfield grass Tuesday and will run the bases either Thursday or in Houston on Friday. He will also progress to taking on-field batting practice sometime over the next couple of days.
"We'll want him to take some live breaks at first base and second base and have a little more aggressiveness on the bases," Hinch said.
Until he begins his rehab, Upton will travel with the D-backs throughout their strenuous four-city, 10-game trip. They do not think he will need a long stint in the Minors before returning to the bigs.
"He's only been gone for a couple of weeks," Hinch said. "It comes with timing and rhythm, and we want him to feel comfortable and not have any hesitation at the plate -- or in the field, for that matter."
Byrnes not ready: Outfielder Eric Byrnes, on the DL since June 25 with a fractured left hand, has gone 4-for-12 (.333) with one double and two runs scored in his first three rehab games with Triple-A Reno.
But because Byrnes has been out for nearly two months, the D-backs have no plans to activate him yet.
"Byrnes has played well -- he's gotten a few hits," Hinch said. "We still haven't talked about bringing him back too soon. He's been gone so long, he's going to need significant time down there."
Schoeneweis doing OK: Hinch has stayed in touch with reliever Scott Schoeneweis, who landed on the DL with depression on Aug. 11.
Schoeneweis' wife, Gabrielle, was found dead in the couple's Fountain Hills, Ariz., home on May 20.
The 35-year-old lefty was at Chase Field on Sunday and threw a bullpen session before the D-backs began their long road trip.
"He's holding up fine," Hinch said. "He's doing everything he can to take a collective deep breath in his life.
"We're people first, and players and coaches second. Giving him time away from his job and having him focus on getting the lives of his four children and himself in a good place has been our first objective."
David Gurian-Peck is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.