BOOK REVIEW / HISTORY : A Sweeping, Compelling Account of Nuremberg Justice : NUREMBERG: Infamy on Trial <i> by Joseph Persico</i> ; Viking, $24.95, 496 pages

Adolf Hitler saved us the trouble by taking his own life, and so did Goebbels and Himmler, but the victorious Allies still faced a tough question when Nazi Germany surrendered in 1945: What to do with the other high-ranking Nazis--Hermann Goering, Albert Speer, Rudolf Hess and a dozen or so others--now held in Allied custody?

Put them up against a wall and shoot them, advised Winston Churchill.

Cooler and more calculating heads prevailed, as Joseph Persico shows us in “Nuremberg,” and the Allies resolved to put the worst offenders among the leadership of the Third Reich on trial in the former Nazi shrine-city of Nuremberg. Now historian and biographer Joseph Persico captures both the sweep and the detail of the war crimes trial in an account that sometimes reads like a Ludlum novel.

The Allies were concerned--indeed, almost obsessed--with making a credible case against the Nazis before punishing them. To prevent the Nuremberg trial from become “a victor’s spectacle” and “a high-grade lynching,” as Persico puts it, the Allies afforded the defendants a trial with all the trappings of Anglo-Saxon jurisprudence.

But the larger purpose of the Nuremberg trial, as Persico points out, was moral and historical. Nuremberg was the place for fixing the crimes of the Third Reich in the collective memory of humankind, an opportunity to translate the German bureaucratic euphemisms--”Special Action” and “Final Solution”--into flesh and blood.

“Germany became one vast torture chamber,” declared Robert Jackson, a sitting Supreme Court justice who took the job of chief prosecutor at President Harry S. Truman’s request. “The cries of its victims were heard round the world and brought shudders to civilized people.”

To his credit, Persico manages to compress the vast legal and political machinations of the Nuremberg trial--a Gargantuan and unprecedented judicial exercise that produced a 42-volume transcript--into less than 500 tight pages without sacrificing the colorful details or the subtle nuances.

“Nuremberg” evokes the quirks and foibles of the Nazis who conquered and ruled Europe with unspeakable cruelty. Goering, for example, is revealed to be a dangerously charming sociopath, a bloodstained voluptuary who showered expensive baubles on his jailers and insisted on sleeping in his favorite blue silk pajamas in an otherwise Spartan cell. Tellingly, when Goering’s young daughter was allowed to visit him shortly before the verdict, she asked: “Daddy, when you come home, will you wear all your medals in the bathtub like everybody says you do?’

Persico invests a good deal of time and effort in describing the little scandals and the petty turf wars that raged within the legal bureaucracy of the International Military Tribunal. Persico suggests, for example, that prosecutor Jackson took advantage of the no-wives-allowed rule to conduct an affair with his secretary. And he gives us a play-by-play account of two American prison psychologists who ruthlessly competed with each other to come out with the first book about the Nuremberg defendants.

Persico also concerns himself with the fine points of the judgment at Nuremberg. Was it proper to hang Julius Streicher, he ponders, whose principal crime was the publication of a newspaper filled with anti-Semitic pornography? And why did the judges impose the death penalty on Fritz Sauckel, a Nazi functionary with a blue-collar background who conscripted slave laborers by the millions, and not on Speer, the cultivated technocrat who worked the slave laborers to death in his arms factories?

“In sending Sauckel to die and allowing Speer to live,” Persico observes, “the court, consciously or unconsciously, made a class judgment.”

Persico weighs the equities of the Nuremberg trial, and--although he is not entirely pleased with the legal procedures or the specific verdicts--he declares his approval of its work: “Nuremberg may have been flawed law,” he concludes, “but it was satisfying justice.”

Lest we forget the crimes of Nazi Germany--and lest we entertain any doubts about the ample evidence of those crimes--Persico’s “Nuremberg” shows us that the defendants never even attempted to dispute that torture, enslavement and murder were conducted on a grotesque scale in concentration camps and killing pits all over Europe. They merely competed with each other to shift the responsibility for their crimes to each other or to Nazis who were conveniently dead.

And that is the single most important function of the Nuremberg war crimes trial and, for that matter, Persico’s book: It’s a pointed reminder that the crimes against humanity committed by the Third Reich were rigorously and repeatedly proven by hard evidence during the trial itself.