Except for the widely misunderstood fluke hit "Short People," the public generally has ignored Randy Newman. Among his colleagues, however, he is justly recognized as one of the most gifted and influential songwriters of the '70s. Artists as diverse as Elvis Costello, Paul Simon and Rickie Lee Jones have cited Newman as a favorite songwriter recently. Simon, Jones, Bob Seger, Lindsey Buckingham, Linda Ronstadt and Don Henley all pay tribute to Newman by singing background vocals on his new album, "Trouble in Paradise" (Warner Bros. 23755-1).

"Trouble in Paradise" has all the virtues that have won Newman such respect. Like "Good Old Boys" and "Little Criminals," the new album is loosely organized around a central concept. As Newman says in his press kit, "It sort of hangs together. There are three cities sung about--L.A., Miami and Capetown--all possible paradises, none of which turned out that way." Of course, there are those who still believe these towns, despite their racial conflicts and conspicuous consumption, are utopias in the sun.

Newman doesn't counter this view with earnest protest songs. Instead, he assumes the role of these apologists and exposes their contradictions even as he argues their case. In "Miami," for instance, Newman assumes the role of a loud-mouthed tourist in a loud Hawaiian shirt who just loves the town, though not for reasons usually associated with paradise--cheap dope, cheap women, and low-life gangsters.

In "I Love L.A.," Newman plays a pushy, fast-talking Hollywood hustler who thinks paradise is driving a big convertible past the mountains with a showy redhead in the front seat. Newman isn't a singer so much as a musical actor, and once again he gets his character just right. You can almost see him jauntily waving a joint and telling the out-of-stater in the back seat: "Look at that mountain! Look at those trees! Look at that bum over there, man; he's down on his knees!"

The same character shows up in "My Life Is Good," the album's funniest song. He doesn't want anyone criticizing him because it's plain to see he's found the good life. He's got his own Mexican maid; his son goes to an exclusive private school; he snorts the best cocaine; he even knows Bruce Springsteen personally. When his son's teacher reports a discipline problem, Newman goes into an absolutely hilarious display of outrage: "Hold it, teacher, maybe my ears are clogged or something; you don't seem to realize, my life is good!"

Newman is one of the few white pop artists willing to tackle racism these days. He does it by assuming the role of white racists and presenting their self-contradicting messages. He has portrayed a slave dealer in "Sail Away" and an Alabama segregationist in "Rednecks," and now he is an old South African drinking beer and discussing the race problem in "Christmas in Capetown," the new album's most chilling song. This character defends apartheid but a certain desperation creeps into his conversation. Even his beer drinking doesn't protect him from the memory of those angry eyes staring from a line of black miners.

Newman is celebrated as a lyricist, but much underrated as a composer. He was born into a family of Oscar-winning soundtrack composers, and he has turned that show-music grammar to his own easiest purposes. Combined with rock rhythms and textures, this gives Newman an extensive musical vocabulary. He uses it most eloquently as he fills songs with motifs, melodies and ever shifting moods. His music does not support his lyrics so much as it comments on them. For instance, the staccato piano figure in "Christmas in Capetown" brings out the fear behind the singer's reassuring words, while segues into holiday organ music point out the song's paradoxes. The overbearing rock cliche's define the characters in "I Love L.A." and "My Life Is Good."

Sometimes Newman's music supplies the joke for a song. "The Blues," a duet with Paul Simon, describes a young, middle-class musician lying about how bad his life has been to establish his blues credentials. The tune reveals the lie--the bright pop melody has nothing to do with authentic blues. "Mikey's" is a monologue by a 40-year-old rock fan who's drinking in a bar, complaining about the changing neighborhood and denouncing this "ugly" new wave and funk music. "Whatever happened to the old songs, Mikey," he whines, "like 'The Duke of Earl?' " Newman's compelling synth-funk backing track builds, and eventually overwhelms, the singer's tirade against change.

Newman has a few lapses on his new album. "Same Girl" traffics in the cheap irony of a romantic ballad for a street prostitute; "There's a Party at My House" is a weak rewrite of Newman's "Mama Told Me Not to Come"; "Song for the Dead" is a heavy-handed antiwar protest. Much better is "Real Emotional Girl" with its rich, Gershwinesque chord progressions and its subtle portrait of a woman who swims and drowns in her own emotions.