BOSTON – Faced with the choice between staying with an aging veteran core and rebuilding with much younger players, the Celtics have decided to do a little bit of both.

By agreeing to work on a three-year deal with Kevin Garnett and, it was learned more conclusively, not let Ray Allen go without a fight, the club believes those two and Paul Pierce can be significant contributors to a contending team.

On the other hand, the Celtics also will try to get younger. The plan is to give the aforementioned trio even more rest during the regular season while developing the talents of players like JaJuan Johnson, E’Twaun Moore and rookies Jared Sullinger and Fab Melo.

Avery Bradley, 21, already has made his way into the starting lineup. He replaced Allen, but the Celts aren’t ready to part with the veteran shooter.

The Miami Heat have made Allen a free agent priority, but the Celtics are hoping the fact Miami can offer him much less than the Celtics and the lure of staying with Pierce and Garnett will sway him to stay.

The Celts still are hoping to sign Jeff Green and Brandon Bass, and they’ve made a qualifying offer to Greg Stiemsma, making him a restricted free agent and giving them the option to match any offer he gets.

If the Celtics get Garnett, Allen, Bass, Green and Stiemsma back, they will be over the salary cap but almost certainly under the next threshold.

That means they would be able to use the full $5 million mid-level exception to add another player, rather than the mini-mid-level available to teams with a higher payroll.

Clearly Danny Ainge and his band of basketball mathematicians have surveyed the free agent landscape for this summer and decided there is no great reward for cleaning house and getting far under the salary cap. They weren’t going to get Dwight Howard or Deron Williams, and as all the teams that wound up whiffing on LeBron James will tell you, the overall odds of landing a superstar in that manner are nearly prohibitive.

So the Celtics are going to try to keep their All-Star foundation — which, we shouldn’t forget, includes 26-year-old Rajon Rondo — and redo the walls and fixtures. “It wasn’t a hard decision to make at all,” coach Doc Rivers said. “Economically it makes a lot of sense.”

It would be hard to picture Pierce, Garnett and Allen surviving even one more season while carrying a heavy minutes load, but the idea now is to even better preserve them for the long haul by opening up the rotation.

Though he’ll argue the point, Rivers has been reticent to simply hand out playing time to the youth, saying they have to prove they are worthy of the chance. His point makes sense, but there might be times when the coach has to give someone enough rope to prove he can’t play.