- Guggenheim Fellowship, 1966
- Time Magazine Best Books of the Year list, 1971, for City Life
- National Book Award, Children's Books, 1972, for The Slightly Irregular Fire Engine or the Hithering Thithering Djinn
- Morton Dauwen Zabel Award from the National Institute of Arts and Letters, 1972
- Jesse H Jones Award from Texas Institute of Letters, 1976, for The Dead Father
- Nominated for National Book Critics Circle Award, PEN/Faulkner Award for Fiction, Los Angeles Times Book Prize, all for Sixty Stories, all in 1982
- Rea Award for the Short Story, 1988
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