INDIANAPOLIS — An NCAA commission chaired by Condoleezza Rice and established last year to respond to federal prosecutors’ charges of widespread bribery and corruption in college basketball proposed several reforms Wednesday that would alter the sport’s texture without challenging the longtime requirement that the players be amateurs, uncompensated beyond a scholarship for their talents and efforts.

The commission called for an end to the “one-and-done” rule, which would need the approval of the NBA and its players’ union.

It anticipated potential future payments to players for the commercial use of their names, images and likenesses pending the outcome of court cases.

It proposed allowing regulated contact with agents.

It would overhaul the sanctions system and summer basketball, requiring shoe companies to assume far more “transparency and accountability.”

“The corruption we observed in college basketball has its roots in youth basketball,” Rice said.

The report said: “The levels of corruption and deception are now at a point that they threaten the very survival of the college game as we know it. It has taken some time to get here, and it will take time to change course.”

One-and-done has been a big part of college basketball in recent years, with the best talents playing only their freshman season and congregating at a few programs, notably Kentucky and Duke. The commission said that if the NBA and its players’ union did not change the rule, it would reconvene to consider unilateral alternatives such as freshman ineligibility. The commission did not suggest an alternative to one-and-done.

In a joint statement, the NBA and the players’ union pledged only to continue assessing the rules, conspicuously failing to endorse immediately an end to one-and-done.

The commission also called on the NCAA to establish a new system for summer basketball, so central to the recruitment process, that would keep out the three main apparel companies — Adidas, Nike and Under Armour. And it proposed allowing players who declare for the NBA draft but are not selected to return to college.

Prosecutors said that an Adidas executive and several others with ties to the sneaker giant were central to schemes to bribe players’ families and college basketball coaches to coax top prospects to commit to schools that Adidas sponsored, like Louisville, Miami and Kansas, and later sign with Adidas.

“Adidas welcomes the commission’s recommendations and will continue to work with the NCAA and other stakeholders in a collaborative and constructive manner,” the company said in a statement. “We share the commission’s desire to improve the environment in which we and other apparel companies engage with college and non-scholastic basketball.”

The commission, which included former players (Grant Hill, David Robinson), former coaches, university presidents, the heads of the Association of American Universities and USA Basketball, and others, stopped short of taking on the so-called collegiate model, instead tacitly endorsing the status quo, in which athletes are “students first” and barred from all kinds of compensation, even as college basketball has grown into a multibillion-dollar industry.

“Our focus has been to strengthen the collegiate model — not to move toward one that brings aspects of professionalism into the game,” said Rice, the former U.S. secretary of state, who was chairwoman of the commission and who delivered a prepared statement at NCAA headquarters here Wednesday morning.

Yet the commission also acknowledged that the very corruption it sought to eliminate arose in part because of the substantial sums players can generate for high school teams, agents, money managers, college teams, coaches and shoe companies, and how this collided with NCAA rules prohibiting players from taking money beyond a scholarship and related costs of attending school.

“Millions of dollars are now generated by television contracts and apparel sponsorship for the NCAA, universities and coaches,” the report said. “The financial stake in success has grown exponentially; and thus, there is an arms race to recruit the best talent — and if you are a coach — to keep your job.”

For this reason, Rice expressed tacit approval for providing athletes with a cut of the commercial use of their names, images and likenesses, which is currently before courts.

The committee also proposed regulating summer basketball, which serves as primary recruiting grounds, so that by 2019 new programs administered by the NCAA are the only ones college coaches are permitted to attend.

Noting that the corruption scheme outlined by federal prosecutors included the use of phony purchase orders to use Adidas money to pay players’ families illicitly, Rice said: “These public companies should be concerned about how their money is being used. I have served on quite a few public boards, and I can tell you, this should be an area of concern.”

The committee suggested allowing limited, regulated contact with agents, starting in high school, to help prospects make decisions about the NBA.

The associationwide Board of Governors and the Division I board of directors were expected to review the recommendations. Legislation designed to implement them could then be written and passed as soon as August. NCAA president Mark Emmert has said he is aiming for results “by tipoff 2018.”