Swingman Jan Vesely, center, is one of the top players who could be available when the Wizards draft sixth on Thursday night. (MINDAUGAS KULBIS/AP)

It was do-over day at Verizon Center on Tuesday, as two players — Jordan Hamilton of Texas and Georgetown’s Chris Wright — were given a second opportunity to make a first impression on the Washington Wizards. The time for the Wizards to take the next step in their rebuilding process is drawing near with the NBA draft set for Thursday at Prudential Center in Newark.

The hard part was already handled last season. The Wizards lucked into their primary building block by winning the No. 1 overall pick and drafting point guard John Wall, a player who mostly lived up to expectations as he had a rookie season comparable to the first years of current all-stars at his position. Now, the team has been assigned to surround him with the right mix of talent that can best exploit his strengths as a speedster who aims to please with his pass-first mentality.

The Wizards brought in nearly 60 players to try out the past two months — including a few repeats — with the team holding three of the top 34 picks in the draft, and President Ernie Grunfeld revealed that the team will likely use the sixth overall choice to improve its depth up front.

“We’re probably looking for a bigger player if possible,” Grunfeld said after the team conducted two workouts on Tuesday morning. “But you never know. If somebody slips to us — and it could be a guard that we have ranked a lot higher — it could be somebody that we take a close look at. But in all likelihood, we’ll be looking for a front-court player if possible.”

Rumors continue to swirl about the Wizards possibly moving up, and Grunfeld didn’t deny that he has spent countless hours talking with other league executives in recent days. He added that talks don’t usually intensify until the hours leading up to the draft, mentioning how the Wizards hadn’t discussed last year’s draft-day trade with Chicago that yielded Kirk Hinrich and the 17th overall pick that turned out to be Kevin Seraphin until two days prior. But if the Wizards keep the sixth, 18th and 34th picks, they have a decent idea of the players who will be available to them.

Turkish forward Enes Kanter, swingman Jan Vesely of the Czech Republic, Lithuanian center Jonas Valanciunas, San Diego State forward Kawhi Leonard and Texas center Tristan Thompson could be around when they draft sixth. Hamilton, Georgia Tech guard Iman Shumpert, Kansas forward Markieff Morris, Southern Cal center Nikola Vucevic, Providence guard Marshon Brooks and Lithuanian forward Donatas Motiejunas — who has an individual workout planned with the team on Wednesday — are possibilities for the team at 18.

The plan is finding the right accessories for Wall — athletic, high-energy players who can run the floor, spot-up shooters who can spread the floor and knock down shots, or big men who can set screens for him in pick-and-roll situations.

“I liked the draft much better last year, when we could just pick whoever we wanted. This year, it’s a little bit different,” Grunfeld said. “We’re looking for players that are team players, first and foremost. Winning is important to these players. Willing to sacrifice for the benefit of the team. And players that we feel can fit into what we want to do. Obviously, we were fortunate to get a player like John Wall, who is a player that can make players around him better. A pass-first type of player. And, he can create some opportunities for his teammates. And we’re trying to get players that complement him, as well as our other young players.”

Grunfeld would not talk about specific players, but said that the Wizards are looking for certain qualities in the players they plan to select. “We’re always looking for good character for your players and that always plays a key role, no matter what type of draft you’re going through. You’re looking at the total package. Can they play? Are they athletic? Are they versatile? Are they team players? Do they have good character? All those things come into play,” he said. “But you look for all types of players. We’ll try to get a balance.”

The workouts have been helpful with the evaluation process but Grunfeld said decisions are rarely swayed completely by what a player does during an hour or so of drills. He uses them mostly to test a players’ endurance, conditioning and level of concentration. The draft board might get adjusted slightly, but rarely do big leaps or huge falls follow the workouts, Grunfeld said. One team insider shared a story about how a player was crossed off consideration last year after he fell asleep in the lounge shortly after a workout.

“You want to know the players, you want to see how quickly they pick things up, but we’ve followed them throughout their whole careers,” Grunfeld said. “We’re going to continue having our meetings and our conversations. Keep going over and over our draft board. We’ve been talking about these players for the last two, three months, and things have intensified.”