Mike Miller was a luxury the Heat decided they could no longer afford.

Miller was designated yesterday as the team’s amnesty player, a move that may save the Heat more than $30 million in luxury tax payments over the next two years.

With the team’s tax bill set to be bigger than ever — depending on what the final payroll numbers are, the Heat could pay as much as $2.50 per $1 they are over the salary-cap threshold for this coming season under the league’s new and more punitive rules — the team ultimately made the call to part with Miller, who would have made $6.2 million this season, and $6.6 million next season. He still gets that money, but his salary will not count against Miami’s cap.

PISTONS: Chauncey Billups is back, and he’s eager to be more than just a mentor.

Detroit brought Billups back on a two-year deal for $2.5 million each year. The five-time All-Star turns 37 in September.

Billups tore his left Achilles tendon during the 2011-12 season, when he was limited to 20 games with the Clippers, and he played 22 games for them last season.

BUCKS: Milwaukee waived forward Drew Gooden and designated him as their amnesty player.

Gooden had two years and about $13.4 million remaining on his contact. He still receives the money, but it doesn’t count for salary cap purposes.

MAVERICKS: Rookie guard Shane Larkin has undergone surgery to repair his broken right ankle. Recovery time is expected to be about three months.