Packers cornerback Davon House has been out almost a month with a dislocated shoulder suffered in the first preseason game. He only just returned to practice this week and is wearing a restrictive brace to protect the shoulder. During Wednesday’s practice, he dropped two out of the four passes thrown to him during a defensive backs drill and looked encumbered by the harness.

Coach Mike McCarthy wouldn’t officially rule House out for Sunday’s season opener against the 49ers, but it seems improbable the second-year cornerback will be on the field. Still, McCarthy insisted that Thursday’s practice, the first that House truly participated in, was another part of the process and said House’s presence on the field was still beneficial.

“There’s great value in having Davon back out there because he was having such a strong training camp, so he’s getting more and more comfortable being out there, going through some of the drills,” McCarthy said. “[We] tried to do a little more with him today because he was in pads. Hopefully he keeps progressing.”

House said wearing the brace “sucks” and explained that it severely restricts his range of motion. Essentially, he is playing with one functioning arm. He’s still aiming to play Sunday, though.

“Hopefully," he said, "I’m praying for Week 1."

Right cornerback job still open: Whether it’s a ploy or not, McCarthy has yet to announce a starting right cornerback. It’s possible he’s withholding the information strategically to keep the 49ers in the dark for their preparation. But it seems more likely that there just isn’t a clear-cut winner at the most competitive position battle of training camp.

House was the early leader before getting hurt. Physical Jarrett Bush and speedy Sam Shields are jockeying for the spot now, as rookie Casey Hayward has fallen behind them. Shields said Wednesday he hadn’t been told anyone had claimed the position; starting left CB Tramon Williams said, “You can’t just stop the competition because the competition has been so good … why not keep it going?”

Bush seemed to be ahead last week, but Shields was terrific in the final preseason game. Against the bruising, run-first 49ers, it may be Bush who sees his name in the starting lineup. Ultimately, of course, the Packers play their five-defensive-back nickel package so much that it doesn’t really matter who starts in the base defense.

Starks still out: Like House, RB James Starks was injured in the preseason opener and has been out for nearly a month. His turf toe has kept him sidelined indefinitely; it’s a tough injury to rehab because it’s so indeterminate. He hasn’t practiced and is out for Sunday’s game. But he did some work inside the Packers indoor facility on Thursday, and after practice, McCarthy said Starks was progressing.

“He’s actually improving," McCarthy said. "I had a chance to watch his rehab on Monday. I did not today. But he’s running. He’s getting better. But as far as next week, I can’t give you an estimate on that."

Good health a burden: The Packers had as many as 21 players sidelined with injuries at one point during training camp. The fact that just two -- Starks and LB Jamari Lattimore (ankle) -- didn’t practice Thursday should have been a welcome sight for coaches, but McCarthy said, “I would classify us as not extremely healthy." He also said the Packers’ overall increase in available bodies presented tougher personnel decisions come game day.

“It’s easier when you have a couple players that may not go,” he said. “But yes, 53 to 46 is always difficult, because obviously everybody wants to play. You’d like to play them all. But that is part of the challenge. My outlook on having a healthy 53, it makes for better practice, and your practice week is very important in your preparation.”

Follow Packers reporter James Carlton on Twitter: @CBSSportsNFLGB and @jimmycarlton88.