Williams, whose ancestry was part black-American, part native American- Indian, was known as the "Big Cat" because of his languid, deceptive ring style. He could also hit exceptionally hard - and in his peak years at the end of the 1950s was considered a possible future world heavyweight champion. That's when the bad luck began to set in.
He was in line to fight the world titleholder Floyd Patterson, whose jaw was far from resilient against big hitters. However, Patterson was paired with the Swede Ingemar Johansson, and lost the title dramatically - knocked down seven times in three rounds - in June 1959. Instead of fighting for the title, Williams took on Sonny Liston twice and was knocked out twice.
He was a huge attraction in Houston, but was always temperamental. On one visit to London he pulled out of a fight with the Welsh heavyweight Dick Richardson because he felt he had heard a message from God telling him not to box.
By November 1964 he was still only 31, which is far from ancient for a heavyweight. But he grew old overnight. The World Boxing Association wanted him to box for their title, which they had stripped from Muhammad Ali on a technicality. The WBA didn't mean much at the time - everybody knew Ali was the best heavyweight in the world - but it provided a way out of the pack for those who were condemned to operate in Ali's shadow.
The WBA paired Williams with Ernie Terrell of Chicago, a 6ft 6in giant who was cunning and awkward inside the ropes but not much of a puncher. It was a fight Williams and his manager Hugh Benbow considered well within his grasp. Benbow told Williams to keep his mind organised, to stay out of the gym for the last couple of weeks once the hard work was done and to keep away from the beer and bright lights which had begun to attract him all too often. Williams, said Benbow, was in magnificent shape only 14 days before the scheduled date.
The Big Cat's luck turned again, however, and once again he was snared by that old habit of being in the wrong place at the wrong time. On the night of 29 November, he was in his car with another man and two women on a country road near Houston known as Jackrabbit Road, when they were pulled over by a Texas Highway Patrolman named Dale Witten. Witten said the car was weaving. When he spoke to Williams he decided the big man was drunk.
Williams said he wasn't. He had been drinking, he admitted, but was perfectly in control of himself. He had merely laughed and shaken when one of the women told a joke. Witten remained unimpressed and arrested him. As they drove back to Houston, Williams said he realised he was being taken to an area of town named Tomball, which as he put it was "tough on black folks".
Williams protested and later said Witten pointed his gun at him. "I grabbed the muzzle, pushed it into the seat . . . it went off and hit me." The police bullet went through his intestines and lodged in his pelvic bone. The boxer said he found himself lying on the road, drifting in and out of consciousness. "I heard one voice, which said: `I'm not gonna put that nigger in my car.' "
Always a religious man, he also said he felt the presence of God protect him from death. "I saw the eternal light God has for man," he told the Dallas writer Mark Seal 20 years ago. "And I was sinking into the darkness of hell until I felt a great big hand on my right shoulder pulling me back to life." He said he heeded the message and tried to put his life in order, but there was nothing he could do to prevent his decline. The bullet remained in his body.
Eventually, Benbow managed to negotiate the by-then 33-year-old Williams a world heavyweight title fight against Ali in the cavernous Houston Astrodome on 14 November 1966. Although there were those who felt the Big Cat was exactly the kind of puncher to expose the young, brash champion, Benbow and Williams understood. He just didn't have it any more. Ali was at his peak, but in Houston the mood was heavy with antagonism towards the man who had embraced the black Muslim movement and refused to take his place with the nation's young in Vietnam. Williams suddenly found himself cast in the role of hero. There was a will for him to win, not just in Houston or Texas, but across America.
It proved horribly misplaced. With his back against the moral wall, Ali was at his most ruthless. He scarcely missed a punch. Williams was down four times before the slaughter was stopped in round three. Benbow said Williams panicked and, a terrible crime for a professional fighter, lost his nerve. In the dressing room Benbow swore at him. "All the ballyhoo scared him to death," said his manager.
Williams retired, couldn't keep up the payments on his house and forfeited it, saw his marriage fail and took a job on a building site. The need for money also forced him to return to boxing until 1972, when he was 39 years old. The last of his 92 fights was one of his 78 wins, over a journeyman named Roberto Davila in Denver.
In his sixties his kidneys failed and he needed regular dialysis. However, the end was premature, the last tragic moment when he was in the wrong place at the wrong time. As he was crossing the road after a visit to hospital, he was knocked over by a car and died from his injuries.
Cleveland Williams, boxer: born Griffin, Georgia 30 June 1933; married (one son); died Houston, Texas 3 September 1999.