Former Alabama football players say the school's No. 1-ranked football program has tried to gain a competitive edge by encouraging some underperforming players to quit the team for medical reasons, even in cases where the players are still healthy enough to play.

At least 12 times since coach Nick Saban took over the program in 2007, Alabama has offered players a "medical" scholarship, according to public statements made by the team. These scholarships, which are allowed under NCAA rules, are intended to make sure scholarship athletes who are too injured to play don't lose their financial aid. A player who receives one of these scholarships is finished playing with that team.

Three Alabama players who've taken these exemptions say they believe the team uses the practice as a way to clear spots for better players by cutting players it no longer wants. These players said they believe Mr. Saban and his staff pressure some players to take these scholarships even though their injuries aren't serious enough to warrant keeping them off the field.

"I'm still kind of bitter," said former Alabama linebacker Chuck Kirschman, who took a medical scholarship last year. Mr. Kirschman said Mr. Saban encouraged him to accept the scholarship because of a back problem that he believes he could have played through. "It's a business," Mr. Kirschman said. "College football is all about politics. And this is a loophole in the system."

Alabama isn't the only school that has given players medical scholarships. Including the Crimson Tide, the 12 members of the Southeastern Conference have given at least 25 of these scholarships to football players in the past three years. Ultimately, it's the school's decision whether a player is healthy enough to play football.

In a statement, Doug Walker, the school's associate athletic director for media relations, said Alabama's first priority in these situations is always the health of its players. "Decisions about medical disqualifications for student-athletes are made by medical professionals and adhere to the parameters outlined by the NCAA…and the Southeastern Conference," he said in the statement.

The school added that the "process for medical disqualification is very similar from campus to campus across the country." Alabama said that student-athletes sign a medical-exemption certificate agreeing that they fully understand the conditions, that the diagnosis of the injury or illness clearly appears to be an incapacitating one, and that there's a "reasonable expectation" they'll never again be able to play.

An Alabama spokesman said the school won't discuss individual cases, citing health-privacy laws. Mr. Saban declined to comment.

How college-football teams manage their allotted number of players is a serious competitive issue in the sport. The 120 schools in the NCAA's Football Bowl Subdivision, the sport's highest echelon, are limited to 85 scholarship athletes each. No more than 25 new signees are allowed to join a team in the fall. Because injuries are common, teams do whatever they can to make sure those spots are filled by the best athletes.

Because some players may fail to qualify academically, some teams take on more players than they have room for, to make sure they don't get caught short. The problem for teams comes when the numbers don't work out and the team winds up needing to make cuts.

Alabama, which won the national championship last season, is off to a dominating 3-0 start this year, including a blowout win over Penn State. The Crimson Tide play at No. 10 Arkansas Saturday in the weekend's most anticipated game.

The program is one of several in the SEC that have developed reputations for pushing roster limits. Since Mr. Saban took over as coach after a stint with the NFL's Miami Dolphins, Alabama has routinely had to trim its roster ahead of the season. Placing players on medical scholarships has helped it do so.

In some cases, the players who took these scholarships say they didn't feel pressured. Charles Hoke, a former Alabama offensive lineman who took a medical scholarship in 2008 because of a shoulder problem, said the choice was left entirely up to him and was based on the many conversations he had with the team's doctors and trainers over the course of his junior year.

Others who took these scholarships say they believe the school is violating the spirit of the rule. Mr. Kirschman, the linebacker, said he injured his back in April 2008 but continued practicing with the team through the spring of 2009. That May, he was approached by coaches and trainers and asked to take a medical scholarship.

"I wasn't playing significant minutes, but I was personally upset because I did anything coach asked, I was a team player, I had a 4.0 average," said Mr. Kirschman, who played in two career games, both in 2008, and is now working full time as a robot programmer at Mercedes.

Mr. Kirschman said the school offered in the summer of 2009 to pay for his graduate degree in business—an offer he accepted—and that he still gets some of the same perks as players. "I still get game tickets, which is nice," he says.

Mr. Kirschman said the decision to take the medical scholarship was ultimately his, and that he decided to do it to open up a scholarship for the good of the team. But he said he felt he was pressured. "It was pushed," he said. "It was instigated for several players."

In August 2009, Jeramie Griffin, a redshirt sophomore running back at Alabama, tore an anterior cruciate ligament in his knee during a practice—an injury that kept him out for that season. After undergoing surgery, he said, "I came back in the spring and I was OK."

Indeed, Mr. Griffin's bio on Alabama's official athletics website said he "looked strong in 2010 spring drills, just eight months off of surgery."

Mr. Griffin said that he was surprised last month when the football staff told him he had failed a physical. At that point, Mr. Griffin said, Mr. Saban sat him down and asked him what he wanted to do besides playing football. He said that Mr. Saban floated the possibility of a medical scholarship and asked if Mr. Griffin was interested in student coaching.

Mr. Griffin said he doesn't contest the results of the physical and said it was "basically my decision" to forgo the rest of his playing career.

Mr. Griffin said he has agreed to take a job as a student coach. He added that he felt less angry about being pushed to take the medical scholarship—which frees up roster space for the team—than he did about not living up to his potential.

"I felt like I could have played," he said.

Write to Hannah Karp at hannah.karp@dowjones.com and Darren Everson at darren.everson@wsj.com