BOSTON >> One parent, hoping to avoid prison in the nation’s largest-ever college admissions fraud case, stood before the judge with an elaborate proposal for a community service project: He could make amends, the parent’s lawyers offered, by designing and raising funds for a “cutting-edge” collaboration between the Special Olympics and private schools.

To reinforce the point, he submitted a polished video recounting his past charitable work, featuring praise from Special Olympics officials, montages of celebrating athletes and a gold medalist describing the defendant as “my neighbor and my best friend.”

Another father submitted a 34-page report from a sought-after Los Angeles criminologist and court consultant — whose past clients include Tupac Shakur and Mike Tyson — detailing how a difficult childhood had left the father susceptible to being manipulated into joining the corrupt admissions scheme.

Sentencing has begun for parents who have pleaded guilty to using their wealth to boost their children’s chances: paying to rig entrance-exam scores, securing athletic-recruit status through bribery. Now some of those parents are using their resources to boost their own chances of getting a lenient sentence, by marshaling the best possible experts and the best possible arguments, some of which bear a trace of the extracurricular resume-polishing of college applicants.

One parent has hired a consultant to tell his life story. Others have obtained letters from doctors and submitted them under seal. Some have pointed to the losses they have already suffered — of high-paying or fulfilling jobs, of once-sterling reputations — to make a case for lesser punishments.

The strategy is not without risk.

“That case is already a case about privilege,” said Shon Hopwood, an associate professor of law at Georgetown University, “and so, if I was the defense team, I would be very careful about how I present it in a courtroom.”

Judge Indira Talwani of the U.S. District Court for the District of Massachusetts, who is sentencing most of the parents who have pleaded guilty in the case, has expressed impatience, and even incredulity, at some of the arguments and materials presented to her.

The parent who proposed the community service project, Devin Sloane, is a Los Angeles businessman who acknowledged that he arranged photos of his son posing in freshly purchased water polo gear in the family pool, as part of a $250,000 scheme to get him admitted to the University of Southern California by passing him off as a recruit for the water polo team.

When one of Sloane’s lawyers told the judge that his proposed project, in which private school students would play sports with children with disabilities, would bring “the values of inclusion, anti-bullying and diversity directly to the independent school children, who are the focus of this case,” Talwani stopped him, saying that the remarks were “about as tone-deaf as I’ve heard.”

She also expressed irritation at the report from the criminologist, which was submitted by Stephen Semprevivo, another Los Angeles businessman. Semprevivo has admitted that he paid $400,000 to get his son admitted to Georgetown as a tennis recruit, even though the son did not play tennis competitively.

Anticipating that other parents scheduled for sentencing in the weeks ahead might follow Semprevivo’s lead and hire similar consultants, Talwani warned: “I maybe should say to you, before I get nine more of these: I don’t feel I need an expert report from a criminologist to tell me how to rule here, particularly where it’s the same criminologist that’s going to be probably presenting for everybody in LA.”

Hiring consultants for criminal sentencings is perfectly legal, and former prosecutors said they did not fault defendants for drawing on expert help to try to avoid going to prison. Lawyers for poor defendants also sometimes submit videos or reports from sentencing consultants or mitigation experts during sentencing. But public defenders and court-appointed attorneys have limited budgets for commissioning such materials.

Talwani sentenced Sloane and Semprevivo, who were among the first parents in the case to be sentenced, each to four months in prison — less than prosecutors had sought, but more than defense lawyers had argued for. Each man had pleaded guilty to a single count of conspiracy to commit mail fraud and honest services mail fraud; the judge calculated that the four-month sentences fell within federal guidelines.

Actress Felicity Huffman — whose lawyers commissioned and submitted a statistical analysis of sentences for similar defendants — was sentenced to 14 days in prison for conspiring to cheat on her daughter’s SAT exam.

A lawyer for Semprevivo did not respond to questions about his sentencing presentation. One of Sloane’s attorneys, Nathan J. Hochman, defended Sloane’s proposed community service project and said it was an effort not to avoid punishment but to give back to society in a substantive way.

“The judge has 11 parents to sentence,” Hochman said of Talwani. “Let’s say that instead of giving each of them 14 days to 6 months in prison, she gave each parent 2,000 hours of community service. Imagine what 22,000 hours of very productive, hands-on community service could do for society.”

Another group of 19 parents, including actress Lori Loughlin, who is accused of paying bribes to get her two daughters admitted to the University of Southern California, is fighting the charges. Those parents’ lawyers appeared in court Wednesday to discuss the progress of the case.

Harry Sandick, a former federal prosecutor and a partner at Patterson Belknap Webb & Tyler in New York, said materials like sentencing videos or reports by sentencing consultants can give a judge a fuller picture of a defendant and put a crime in context.

Thanks in part to smartphones, which make it easier for people to make simple videos, there is “some leveling of the playing field,” Sandick said. But the risks, he said, are clear: “You don’t want to create the impression that this is an attempt to manipulate the judge — that it’s too glossy.”

Hopwood, the Georgetown law professor who spent more than a decade in prison for bank robbery before going to law school, said the purpose of a sentencing video was “to make the judge sweat” — for example, by showing the young children who would be affected by a parent going to prison. But he said he had seen some sentencing videos “that look like they came from a Hollywood production team,” and he did not think that was helpful.

The criminologist who wrote the report for Semprevivo, Sheila Balkan, said she focuses on humanizing a defendant and on proposing how the defendant can best be rehabilitated and pay a debt to society. She often helps get defendants into treatment programs and community service projects even before they are sentenced.

“I’m helping somebody rebuild their life, whether or not they are incarcerated,” she said.

Prosecutors in the admissions case have tried their best to turn the defendants’ sentencing presentations against them, suggesting that they point to a lack of contrition and a determination to avoid punishment. It appeared that some parents were getting the message that introducing extensive consultants’ reports could backfire. Materials submitted by defendants scheduled to be sentenced in the coming days appeared more restrained than those handed in for earlier parents. In some cases, the defendants and their attorneys even underscored their decision to reject expert help.

Today, Gordon Caplan, a former co-chairman of a major New York law firm who pleaded guilty to paying $75,000 to cheat on his daughter’s ACT exam, appeared in court. He had submitted letters under seal from two psychiatrists and a psychologist, and his lawyers said in a sentencing memo that Caplan had already been punished significantly by losing his job and his ability to practice law, at least for some time.

But at the sentencing, one of Caplan’s lawyers, Joshua S. Levy, said, “He’s absolutely not making any argument to the court that he should get a lighter sentence because he comes from wealth or prestige — that’s a repulsive argument.”

Talwani ordered Caplan to serve one month in prison.

Agustin Huneeus, a Napa Valley vintner, who participated in both the test cheating and bribery schemes on behalf of his daughter, is scheduled to be sentenced Friday. Prosecutors have argued that his conduct was especially egregious and that he should be sentenced to 15 months in prison.

Huneeus’ lawyers argued in their sentencing memorandum in favor of two months of incarceration, plus a fine and community service. They drew a contrast between their client and the parents who have already gone before the judge.

Huneeus, they noted, “has not hired experts (psychologists, criminologists or others) to explain or contextualize his conduct.”

And Gregory Abbott, who is scheduled to be sentenced next week, along with his wife, for engaging in the test cheating scheme, began his letter to Talwani by assuring her it was written without outside assistance.

“Despite the several ‘consultants’ who solicited me, insisting I needed them,” he wrote, “the following words are totally my own, as they should be.”