Hajdu (an editor at Entertainment Weekly) has found a perfect subject in Strayhorn, a little-studied figure central to jazz history, the composer of such famous Ellington-band pieces as ``Chelsea Bridge,'' ``Lush Life,'' and ``Take the A Train.'' ``Strays'' (also known as ``Swee' Pea''), born in 1915, grew up working-class in Pittsburgh and had high-society aspirations from the start: He wrote an entire Gershwin-like musical revue a year out of high school, full of sophisticated recitative and advanced harmony. He yearned for a career in concert music. But, as Hajdu points out, he was a ``triple minority'': black, gay, and unwilling to hide his homosexuality. His break came in 1938, when he met Duke Ellington; possessed of both a supernal cool and a tenacious business sense, Ellington knew Strayhorn was gifted and worked out a deal. Hajdu meticulously recreates this unusual agreement: Ellington gave Strayhorn free rein to let his Ellington- influenced composistional sense run wild, but he gave Strays no by-line (and, as Strayhorn would find out, no publishing royalties). At first, Strayhorn submitted to Ellington's benevolent dictatorship. Eventually, though, his compositions moved beyond Ellington's influence; as he grew increasingly depressed by his obscurity, he transcended the ghost-writing arrangement to achieve his own, dark style and a small measure of fame. As one of his friends told Hajdu, both Ellington's and Strayhorn's music was great, the difference was that Strayhorn's ``was so full of feeling.'' This is jazz history as it has seldom been written before, covering both Strayhorn's powerful music and difficult life as well as the hidden history of New York's black and gay artists from the 1930s until Strayhorn's death in 1967. Hajdu gets deeply felt and non-mythologizing input from important members of Strayhorn's protective circle, including ex-lovers and close friends (Lena Horne's reminiscences are extraordinarily moving). A good idea done right.