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Even with their exciting new point guard, the Utah Jazz are entering free agency with more holes and questions than could be addressed in a draft worthy of praise.

"I think clearly shooting is a priority," general manager Dennis Lindsey said in the hour after the Jazz's trade for Trey Burke was announced Thursday night. "I think some veteran leadership is another thing Ty probably wants relative to the youth of our club."

At that, Ty Corbin, the Jazz's fourth-year coach, began to nod.

Starting Sunday at 10 p.m. MDT, NBA teams were allowed to begin negotiating with free agents, although players can not be signed until July 10. The Jazz's top priority will be filling out a roster that, including the three draft picks, consists of eight players. The average age of those eight? Twenty-two years, 276 days.

What players the Jazz will target, however, remain a mystery.

The big question facing the Jazz is how to balance the young core of Burke, Gordon Hayward, Derrick Favors and Enes Kanter, and the clear need for veterans at every position.

Seven players from last season's 43-39 team are bound for free agency, and veterans such as Al Jefferson, Paul Millsap and Mo Williams are expected to test the market and will most likely sign elsewhere.

Jefferson and Millsap will likely both be out of the Jazz's price range, and signing either to a long-term deal could impede the development of young big men Kanter and Favors. Jefferson is seeking a maximum contract and is considered by some to be the top free agent in the class behind Dwight Howard and Chris Paul.

The salary cap increased to a reported $58.5 million, giving the Jazz more than $30 million in cap space before they sign Burke, and fellow draftees Rudy Gobert and Raul Neto. While the Jazz have as much money to spend as anyone in the league, don't expect them to, as your parents warned, spend it one place.

Lindsey and others within the Jazz organization have long praised the flexibility this offseason gives them, not just for this offseason, but for the future. Absent adding a franchise player, it's unlikely the organization will add a long-term, big-bucks contract and stunt the growth of its young core.

Most intriguing may be what the Jazz do at point guard. Burke was drafted to eventually become the starter, but the Jazz have a long history of bringing point guards along slowly.

"We'll see what the response is on the free agent market," Lindsey said. "We'll do our due diligence, we'll be aggressive, and if there's a great player that plays that position that wants to come to Utah, we think we have a lot to offer on a lot of different levels."

Unrestricted free agents Randy Foye and DeMarre Carroll have both publicly said they hope to stay with the Jazz, while sources told The Tribune that 35-year-old point guard Jamaal Tinsley would also like to re-sign and serve as a mentor to Burke.

The Jazz could target players such as former Jazz forward Kyle Korver, or any number of his Atlanta Hawks free-agent teammates. Andrei Kirilenko, an All-Star for the Jazz in 2004, opted out of $10 million in Minnesota over the weekend but is not expected to be a Jazz target, according to a source.

According to multiple reports Sunday afternoon, the Jazz are interested in Dallas shooting guard O.J. Mayo.

Asked at which positions it would be most important to add veterans, Corbin said that wasn't as important as "much as people."

"The main thing," he said, "is the fit has to be right for where we are within our development now."

The Jazz need depth at every position. The acquisition of Burke likely keeps the Jazz out of the hunt for one of the top point guards available, such as restricted free agents Jeff Teague and Brandon Jennings.

Lindsey said Thursday he was "not totally pleased" with the Jazz's preparation for free agency.

"We were trying to run [free agency and the draft] on parallel tracks," he said. "I'm not sure we did a great job of it. ... We tried to throw scenarios of this and the draft, and so I think we'll be prepared once July 1 comes about who we want to call first and where our objectives are."

boram@sltrib.comTwitter: @tribjazz —

Jazz free agents

• Al Jefferson, center

• Paul Millsap, power forward

• Earl Watson, point guard

• Mo Williams, point guard

• Jamaal Tinsley, point guard

• Randy Foye, shooting guard

• DeMarre Carroll, small forward

Top free agents available

Centers

1. Dwight Howard, Los Angeles Lakers; 2. Al Jefferson, Utah Jazz; 3. Andrew Bynum, Philadelphia 76ers

Power forwards

1. Josh Smith, Atlanta Hawks; 2. David West, Indiana Pacers; 3. Paul Millsap, Utah Jazz

Small forwards

1. Andre Iguodala, Denver Nuggets; 2. Mike Dunleavy, Milwaukee Bucks; 3. Andrei Kirilenko, Minnesota Timberwolves

Shooting guards

1. Monta Ellis, Milwaukee Bucks; 2. Tyreke Evans, Sacramento Kings (R); 3. Manu Ginobili, San Antonio Spurs

Point guards

1. Chris Paul, Los Angeles Clippers; 2. Jeff Teague, Atlanta Hawks (R); 3. Brandon Jennings, Milwaukee Bucks (R)

Other notables: Tony Allen, Memphis Grizzlies; Jose Calderon, Detroit Pistons; J.J. Redick, Milwaukee Bucks; Nikola Pekovic, Minnesota Timberwolves (R); Tiago Splitter, San Antonio Spurs (R); Carl Landry, Golden State Warriors; Beno Udrih, Orlando Magic; Devin Harris, Atlanta Hawks

(R) = Restricted free agent