Early in 1991, the Decca record company took what may go down as the most enlightened decision in a century of commercial music. Awash with profits from "The Three Tenors in Concert" (1990), executives were wondering how to invest the windfall when a young American producer, Michael Haas, came up with a dazzling concept: bring back the music that was banned by the Nazis.

This was not going to be an easy sell. Hitler had damned as entartet, or degenerate, music by Jews, atonalists, modernists, jazz-makers and political enemies. Dozens of composers were erased from history, never to return. Some were murdered, others were pushed into the oblivion of exile. After the war, former Nazis held influence in German music and young musicians, unwilling to look back, upheld the banishment across the classical-music spectrum. Mr. Haas was proposing an act of cultural restitution on a scale never attempted before.

Decca's president at the time was a German, Roland Kommerell, whose uncle had worked with the profoundly compromised philosopher Martin Heidegger. Komerell got the point and gave Mr. Haas the green light for a series titled Entartete Musik.

Where to begin, among the long-forgotten? Mr. Haas collected 300 composers' names from prewar publishers' catalogs but struggled to find scores and assess merit. Who knew if such 1920s hits as Ernst Krenek's blackface jazz opera "Jonny spielt auf" and Erich Wolfgang Korngold's "Das Wunder der Heliane" would appeal to modern ears? Why did Walter Braunfels, a devout Catholic, get banned? Did the expressionist Franz Schreker deserve the punning epithet schrecklich (dreadful)?

Mr. Haas took his lists to Berthold Goldschmidt, an octogenarian living near Hampstead Heath in London, only to discover that this long-neglected composer, besides having perfect recall of Weimar-era music, was one of the unluckiest victims of the ban. Hailed by a critic in 1932 as "the white hope of German music," with an opera premiere heading for Berlin the following year, Goldschmidt lost everything when Hitler came to power. In his English refuge, he was known chiefly for helping to complete Mahler's 10th symphony. Entartete Music reversed his fortunes. By 1996, when he died at age 93, Goldschmidt had heard all of his forgotten music recorded and was busy composing more.

Decca's restitution was an extraordinary adventure into the unknown. Almost everything that Mr. Haas recorded was novel, unexpected, often unbearably poignant. At a Prague recording of Pavel Haas's effervescent opera "The Charlatan," none could ignore the proximate facts of the Czech composer's fate—incarcerated in the nearby Terezin camp, then gassed, age 45, in Auschwitz. By the time classical recording hit a mid-1990s downturn and cost-cutters pulled the plug on the series, Mr. Haas had produced 31 albums and rewritten a sizable chunk of the verdict of history.

The scale of dispossession defies belief. Goldschmidt told me that he was personally acquainted with more than 100 composers who fled Germany. My hope was that "Forbidden Music: The Jewish Composers Banned by the Nazis" would tell the romantic story of Mr. Haas's quixotic mission. Perhaps prompted by an academic publisher, he decided to cast his net wider and seek to place the Nazi prohibition in a broader context of German cultural anti-Semitism. The first third of the book tell us little that we have not read elsewhere. Oppression begins with the appalling pamphlet "Das Judenthum in der Musik," issued by Richard Wagner under a pseudonym in 1850 and again under his own name 20 years later. In it Wagner claimed that Jews could not achieve originality in German art. Hitler used this charge as his manifesto for cultural cleansing.

By the turn of the 20th century, in Mahler's Vienna, Jews were identified in the public mind with ultra-modernist tendencies, an antidote to the romantic nationalism that had fueled the rise of German music. Arnold Schoenberg's atonalities were an affront to middle-class ears, contradicting the expectation of pleasure. Jews were blamed for the destruction of German certainties. Cleansing was loudly demanded. Mr. Haas finds the term entartet applied to music, perhaps for the first time, by the venerable scholar Guido Adler, a close friend of Mahler's. Adler, in a 1917 essay, calls for "musical boils to be lanced' to stop the spread of "degeneration." By 1920, most of Vienna's leading "degenerates" had fled to liberal Berlin.

There, Franz Schreker, a writer of emotionally overwrought operas, shared with Schoenberg the job of teaching a new generation of German composers. Half-Jewish and unpopular in his profession, Schreker inspired Krenek, Goldschmidt, Max Brand and others to launch a genre of Zeitoper—operas that tackled contemporary social issues. His own operas were overloaded with sexual complications. On his death in exile in 1934, a Nazi critic called Schreker "the Magnus Hirschfeld of music" (a reference to the prominent liberator of sexual minorities) and a man "for whom no sexual perversion could not be set to music." Schreker, his operas first recorded on Entartete Musik, is now enjoying a small revival in decadent 21st-century German Regietheater (i.e., "directors' theater").

Hanns Eisler, raised in Vienna, is a more elusive victim of the era. Moving to Berlin in 1918 after his brother and sister founded the Austrian Communist Party, Eisler fell out with his teacher Schoenberg and succeeded the irascible Kurt Weill as Bertolt Brecht's chosen composer. In exile, he wound up working in Hollywood. There, his sister, Ruth, having rejected her earlier sympathies, denounced him to the House Committee on Un-American Activities, forcing him eventually to flee to East Germany, where he composed the national anthem. Eisler, disillusioned at his death, is slowly making a comeback in German concert halls.

Ernst Toch, once Paul Hindemith's rival for German prizes, joined the flight to Hollywood, where he wrote music for Shirley Temple films. Korngold, who set the benchmark for film music with Errol Flynn swashbucklers and psychological thrillers, was by far the wealthiest and most successful of émigrés. But he never got over his erasure from classical concerts. I have in my possession a letter from his wife, as he lay dying in 1959, begging the BBC to perform his forgotten, forbidden, music.

Mr. Haas crams a vast amount of material into a complex argument that is at times marred by disconcerting leaps back and forth in chronology. He bypasses the foremost exiles—Weill, Schoenberg, Hindemith, Alexander Zemlinsky—and sometimes overstates the value of neglected composers. His chronicle is nonetheless a valuable compendium of untold stories, a corrective to standard histories of music and an essential reference point for anyone engaged in the culture and politics of the 20th century.

Be warned that the risk in reading "Forbidden Music" is that you will lose many hours of your life relistening to the Entartete Musik series and its triumphant restorations. Korngold's violin concerto is now, finally, at the center of concert repertoire. The works of Terezin composers Pavel Haas, Viktor Ullman and Hans Krása are widely played. Hans Gál's symphonies are appearing on record. Eisler is sung all over, and once-forbidden music is seeping into the musical DNA of the 21st century, the Nazi purpose defeated.