Such a message was unnecessary with Allen, who said he increased his running during the lockout to maintain his wind and stay lean. But with the lockout now over, his physical skills could be tested when the Celtics squeeze 66 games into roughly four months.

Commissioner David Stern canceled games because of the labor strife, and with the settlement over the weekend, there is now a 30-day window for a Christmas NBA opening. The Celtics had 24 games canceled, leaving them with 58, so in their case the league will sprinkle eight more games into their schedule, extending the season one more week.

While the veteran Celtics would have benefited if the schedule was picked up on Christmas with no additional games, they will prepare for what is ahead. Luckily, the situation is not as bad as that after the 1998 lockout, when the league played 50 games in roughly 2 1/2 months.

The age issue should not hover over the club during training camp. Allen never allows himself to slip out of shape, Paul Pierce looked lean during his stint in Rajon Rondo’s charity game last week at Harvard, and Kevin Garnett has been playing pickup games in Los Angeles.

Center Jermaine O’Neal, who will play a critical role because of Shaquille O’Neal’s retirement, is eight months removed from knee surgery and played during a Las Vegas league in August.

The bigger issue will be the minutes they log during the regular season. Rivers always has made sure to limit the minutes of Garnett, but he now may have to include Pierce and Allen in that equation.

The question here is the rest of the roster. The Celtics will begin camp Dec. 9 with nine players under their control. Jeff Green is a restricted free agent who will be eligible to field offers from other clubs that the Celtics are expected to match. JaJuan Johnson and E’Twaun Moore are rookies who barely have met Rivers because of lockout restrictions.

The lack of a summer league hurt the Celtics deeply because Johnson, Moore, and Avery Bradley were unable to get any exposure to NBA competition in an organized setting. They will enter camp needing to fill key roles until team president Danny Ainge brings in veterans to compete for roster spots.

Ainge has pulled off some commendable moves before to rebuild the roster, but one of his toughest tasks will come in the next few weeks when he has to add talent to a salary-cap strapped roster. Glen Davis is an unrestricted free agent and after some grumbling about leaving has changed his mind and said he wants to return to Boston.

With the expected free agent frenzy, the question for Ainge is whether to bring Davis back on a one-year deal and allow the hulking forward to become a free agent again next year, when the market will be more predictable and likely more fruitful.

Ainge has to surround the Big Three with younger players who are capable of filling roles. He missed last year with Troy Murphy, Sasha Pavlovic, and Carlos Arroyo. Rivers didn’t trust them, and they ended up sitting on the bench while the coach relied on his aging veterans to run with the Heat.

The Celtics would appear to need guard Delonte West just as much as he needs them. He was working at a Maryland furniture store during the lockout. But when he was healthy last season he contributed significantly. And while the Celtics melted under the Heat’s pressure, West averaged 10.2 points in 23 minutes during the series as the primary backup to Rondo.

If Ainge cannot surround the Celtics’ core with younger players, the abbreviated but packed schedule will have a negative effect and Rivers may have to resort to resting his stars - increasing the chances for losses - to preserve them for the postseason.

While the method worked in 2010, when the Celtics reached the NBA Finals as the fourth seed, the Eastern Conference will be more difficult to conquer with the Heat, Bulls, Knicks, Magic, and Hawks all significantly younger and with more depth than the Celtics.

Ainge unquestionably has prepared for this scenario for the past five months, and there are plenty of free agents such as Michael Redd, Anthony Parker, Sebastian Telfair, Shane Battier, Tracy McGrady, Kwame Brown, and Craig Smith who may accept lesser money for a chance to win a championship.

Playing for the Celtics, with the Big Three and for Rivers, is an attractive enticement that Ainge will use in his bid to sign players over the next few weeks. The NBA announced last night that every team will play at least one and no more than three back-to-back-to-back games.

Making one final run at the NBA title will indeed be a team effort for the Celtics brass, and the concern is more who will relieve the Big Three than whether the Big Three are prepared for the rigors of this unusual season. Pierce, Garnett, and Allen have earned our trust.

Gary Washburn can be reached at gwashburn@globe.com. You can follow him on Twitter at @gwashburn14.