Those close to King, including journalists covering the civil-rights movement, were aware of his womanizing and drinking—though they did not know the extent or, shall we say, the vividness of it. Some of his clerical associates, Mr. Garrow writes, joined him in group sex with women whom, using a private code, they called “parishioners.”

Reporters heard rumors at the time. They talked and sometimes joked about them. But they did not write about such things, for it was a different time, with different rules regarding the privacy of public figures. Reporters didn’t write about Franklin Roosevelt’s wheelchair, either, or about Joseph McCarthy’s drinking or John Kennedy’s sex life.

When King preached to his congregation, he often spoke of himself as a sinner. Unlike some preachers, he meant it. He knew that he was a flawed man. Maybe King’s conscience should be understood with the help of the novelist Graham Greene’s modernist Catholic conceit that great saints may find their path to salvation by way of egregious sins. Some psychiatric speculation suggests that the drinking and the sex were the result of manic depression.

On the exalted, public side of the ledger stands the moral leader who changed America for the better and who knew the price that he would pay for it.