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The Burden of Proof Scott Turow (Farrar, Straus & Giroux, $22.95) Although The Burden of Proof lacks the sure re thriller devices that helped make Presumed Innocent such a commanding piece of storytelling, readers who persevere will be rewarded. B Children of the Dragon: The Story of Tiananmen Square (Collier, $19.95) A handsome collection of photographs, speeches, and newspaper accounts documenting the ill-fated democracy movement in China. B+
Coyote Waits Tony Hillerman (Harper & Row, $19.95) The 11th tale in Hillerman's series about the Navajo Tribal Police is sturdy work from an incorruptible craftsman. A-
Crooning John Gregory Dunne (Simon & Schuster, $19.95) Essays full of high dudgeon and sometimes high reward. B
Crosstown Traf c: Jimi Hendrix and the Rock 'n' Roll Revolution Charles Shaar Murray (St. Martin's, $18.95) The best book yet on Hendrix-and also a sweeping historical discussion of soul, jazz, the blues, and the impact of technology on pop music. A
Etchings in an Hourglass Kate Simon (Harper & Row, $19.95) The third volume of Simon's memoirs (Bronx Primitive, A Wider World) tells how an adventurous, self-sufficient travel writer developed from an insecure existence as wife and mother. A
Get Shorty Elmore Leonard (Delacorte, $18.95) Hollywood has been good to Elmore Leonard, and Leonard has returned the favor with a blackly comic thriller set there. A-
Hit Men: Power Brokers and Fast Money Inside the Music Business Fredric Dannen (Times Books, $19.95) A revealing look at the men who manipulate the rock & roll business. A
Jazz Singing: America's Great Voices From Bessie Smith to Bebop and Beyond Will Friedwald (Scribner's, $29.95) The author's quirks aside, this is quite simply the best available guide to the art of jazz singing. A-
Language Maven Strikes Again William Sa re (Doubleday, $22.95) The sixth collection of Sa re's pun-mongering ''On Language'' columns. B
Out There: The Government's Secret Quest for Extraterrestrials Howard Blum (Simon & Schuster, $19.95) Researched with apparent meticulousness and written with a fine balance of irony and open-mindedness, Out There investigates the U.S. government's 43-year quest for extraterrestrial intelligence. A-
Seventh Heaven Alice Hoffman (Putnam, $18.95) A young divorcee sparks a ( mystifying outbreak of passion in a Long Island suburb. B
Too Good to Be True: The Outlandish Story of Wedtech James Traub (Doubleday, $21.95) As Traub deftly shows us, this is a story not about venality but about human frailty. A
Also Noted American Quest Jack Barth (Fireside Books, paperback, $8.95) Quirky, amusing, American adventures: trying to kiss 10 TV stars from the '60s, working at the Coca-Cola hotline, retracing the trip in Easy Rider.
Bitch, Bitch, Bitch Mike Wrenn & David Wheeler (Dell, paperback, $8.95) Aptly subtitled: ''An unrestrained collection of some of the more vindictive or insulting remarks made by celebrities about each other.''
A Dictionary of the Second World War Elizabeth-Anne Wheal, Stephen Pope, and James Taylor (Peter Bedrick Books, $29.95) From Aachen to Yugoslavia.
The Fireman's Wife Richard Bausch (Linden Press, $18.95) Luminous short fiction from the author of Spirits and Mr. Field's Daughter.
The Flight of the Wild Gander Joseph Campbell (Perennial, paperback, $9.95) The controversial author of The Power of Myth explores the geographical origins of myth.
Holy Terror: Andy Warhol Close Up Bob Colacello (HarperCollins, $22.95) Could also be titled Bitch, Bitch, Bitch.
The Portable World: A Complete Pocket Atlas Edited by B.M. Willett, David Gaylard, and Lilla Prince-Smith (Avon, $10.95) Now yocan carry the world on 272 pages in your pocket.
Sylvia Plachy's Unguided Tour (Aperture, $39.95) This woman's camera has taken her nearly everywhere, and she just can't take a bad picture.
