Mercury Morris, a football star with a drug addiction, seemed hopeless in 1982.

Convicted of cocaine trafficking and sentenced to 20 years in prison, he appeared destined to be remembered more for his crimes than his accomplishments.

But these days, when Mr. Morris flashes an easy smile and talks football, the worst parts of his past never surface.

He has been appearing on ESPN studio shows, reminiscing about his glory days with the 1972 Miami Dolphins, the only NFL team in the modern era to finish a season undefeated. The cocaine case that nearly destroyed him no longer comes up.

Whether big-league baseball players implicated in the steroids scandal can similarly rehabilitate themselves and their images is another question. Many sports figures have overcome crimes, rule breaking and ethical slips. Countless others have not.

Mr. Morris, a Ben Avon native who is now 60 years old, has had one of the remarkable turnarounds. Born Eugene Morris, he took the nickname "Mercury" in college at West Texas State, then carried it with him to the Dolphins.

He helped the team win two Super Bowls and he made three pro bowls. Mr. Morris also became hooked on cocaine, a scourge of the National Football League in the 1970s and early '80s.

A successful appeal of his drug trafficking conviction in 1986 gave him hope. He worked out a deal with Florida prosecutors that set him free. Those watching him on ESPN today have no sense that he hit rock bottom a quarter century ago.

He is hardly the only sports figure who has bounced back from self-inflicted problems.

George O'Leary lied on his resume about having a master's degree and about playing college football. His dishonesty cost him his new job as head football coach at Notre Dame, where he was fired in 2001 after less than a week.

Mr. O'Leary was tarnished, but he remained employable. First Mike Tice, who had played high school football for Mr. O'Leary, hired him as an assistant coach with the Minnesota Vikings.

Then Mr. O'Leary got another head coaching job on a college campus. Administrators at Central Florida, intent on building their program into a national power, said he deserved a second chance.

Athletes caught in gambling or steroid scandals usually have more difficulty than those who lie or use recreational drugs.

Canadian sprinter Ben Johnson is remembered for little except his use of illegal steroids. He won the gold medal in the 100 meters at the 1988 Summer Olympics in dramatic fashion, blazing by American Carl Lewis. But a drug test soon changed the result. The International Olympic Committee stripped Mr. Johnson of the gold.

American Marion Jones this year surrendered the five track and field medals she won at the 2000 Summer Olympics. Her case took longer to play out, but she finally admitted that steroids had helped create her speed and leaping ability.

Like Ben Johnson, she seems likely to be remembered for drug use, not athletic excellence.

Pete Rose gambled on big-league games while managing the Cincinnati Reds. Baseball's commissioner in 1989 suspended him indefinitely and he remains one of the game's pariahs.

Mr. Rose says he is the victim of a double standard. Had he been addicted to cocaine instead of gambling, he says, the major leagues would have paid for his rehabilitation and welcomed him back.

But Mr. Rose insisted for many years that he was an innocent victim, not a man with a gambling problem. He wrote a book with author Roger Kahn proclaiming his innocence. Then Mr. Rose changed his story, dashing off a second book in which he admitted his guilt.

Historically, baseball has shown little tolerance for gamblers. It banned Shoeless Joe Jackson and seven other Chicago White Sox on charges that they conspired with gamblers to throw the 1919 World Series.

A Chicago jury acquitted Mr. Jackson of the fix, but Baseball Commissioner Kenesaw Mountain Landis threw Mr. Jackson out of the major leagues.

Mr. Jackson died in 1951, a baseball outcast. Since then, fans and state legislators in his native South Carolina have argued unsuccessfully for his reinstatement. This designation would allow him to be voted into the Baseball Hall of Fame.

To this day, Mr. Jackson remains better known for the Black Sox Scandal than for batting .356 across 13 seasons.

In contrast, Paul Hornung and Alex Karras reclaimed their careers and reputations after admitting they had gambled on NFL games when they were among football's biggest stars.

NFL Commissioner Pete Rozelle suspended both men for the 1963 season, a decision that gave credibility to pro football and to Mr. Rozelle.

Mr. Hornung, "Golden Boy" of the Green Bay Packers, and Mr. Karras, an all-pro defensive lineman with the Detroit Lions, soon returned to glory.

After his suspension was lifted, Mr. Hornung remained the favorite player of Green Bay coach Vince Lombardi. Writers voted Mr. Hornung into the Pro Football Hall of Fame in 1986.

Mr. Karras became more famous after the scandal. By the 1970s, he was an actor, receiving critical acclaim for his portrayal of George Zaharias, husband of Olympic champion Babe Didrikson. He also punched out a horse in the movie "Blazing Saddles" and had a three-year run as an announcer on ABC's "Monday Night Football."

His life was much richer and smoother than that of Connie Hawkins, the wondrous basketball player whose pro career was cut short by innuendo.

New York City prosecutors linked Mr. Hawkins to a basketball point-shaving scandal in 1961. At the time, he was an 18-year-old freshman at Iowa who had yet to play a varsity game.

The mere fact that the investigation included Mr. Hawkins led the NBA to blacklist him.

This misfortune brought Mr. Hawkins to Pittsburgh. Probably the most underpaid superstar in sports history, he first played for the fledgling Pittsburgh Rens of the old American Basketball League. After the Rens folded, Mr. Hawkins led the Pittsburgh Pipers to the first championship of the now-defunct American Basketball Association in 1968.

Two Pittsburgh lawyers, S. David Litman and Roslyn Litman, helped him reclaim his reputation. They sued the NBA, contending he was being denied employment in the world's premier basketball league because of nothing more than rumors.

In pretrial depositions, the Litmans established that Mr. Hawkins had never been part of any point-shaving or gambling. Trounced in a court of law, the NBA awarded Mr. Hawkins a contract with the Phoenix Suns.

But by then, he was 28 years old with creaking knees.

The NBA in 1996 named Mr. Hawkins one of its 50 greatest players. Even so, he might be better known for his long fight to clear his name.