Maurice Cheeks has a suggestion box.

“I put different names in there,” the Pistons’ coach joked. “People put names in the box, and we figure out which one is the best.”

After Monday’s practice in Auburn Hills, the suggestion box was getting its fill.

A day before the Pistons open the season against the Washington Wizards on Wednesday night at the Palace, they’re still beaten up — especially in the backcourt — but things are getting better.

Italian import Luigi Datome practiced with contact for the first time in a long time Monday. Shooting guard Rodney Stuckey did not.

And with Stuckey still nursing an injured thumb and Brandon Jennings recovering from oral surgery, the backcourt will be in flux early.

“I like to keep guys in their role that they’re going to be playing pretty much this season, rather than trying to jump them out there for something that they may not do,” Cheeks said.

Cheeks said he didn’t know who would start the opener in the backcourt alongside, most likely, Chauncey Billups and if, as expected, Stuckey and Jennings are out.

If the guards were healthy, he said about the backcourt situation: “It would have probably been laid out a little easier now up to this point.”

Could rookie Peyton Siva, who started the final game of the exhibition season, start in order to keep Will Bynum with the second unit?

“Not sure,” he said. “I would rather Will stay in his role. … I like him in the second unit because he moves that scoreboard so well, and playing with Andre (Drummond) like that, I like him in that role.”

Could wingman Kyle Singler start at guard?

“Suggestion box, again,” Cheeks said.

“It’s a dilemma to figure out which way to go because Kyle in his customary role is pretty good in his role, which allows one of the big guys to come out and kind of throws a monkey wrench in it.”

And could Datome, who has impressed the first-year coach with his shooting ability, serve Wednesday as the backup small forward?

“Another suggestion box,” Cheeks said. “That suggestion box is getting filled up.”

He wouldn’t commit to Datome playing Wednesday night, saying he has to go through another full-contact practice.

“Games are totally different,” Cheeks said. “It’s unfortunate he didn’t get the chance to play because it would have been good to see him.”

But he was happy with what he saw out of last year’s Italian League MVP on Monday.

“He got through fine,” Cheeks said. “He was pretty good, too. He made some shots, ran the floor well. He looked good out there.”