It was in my late teens that I fell for Donald Barthelme. No passing adolescent fancy this, but a palpitating obsession of the first water. In his essay The Beards, Jonathan Lethem writes of Talking Heads that "[at] the peak, in 1980 or 1981, my identification was so complete that I might have wished to wear the album Fear of Music in place of my head". In 1993 I felt much the same way about Forty Stories, the first Barthelme collection I owned.

That book and its predecessor Sixty Stories were Barthelme's self-selected "best-ofs", their contents culled from nine story collections and work first published in magazines such as the New Yorker and Esquire. His fiction resulted in more letters of complaint being sent to the former publication than any other writer, a predictable result of its audacity. His postmodernist aesthetic, however, is not of the sort that revels in being problematic for its own sake. "Art is not difficult because it wishes to be difficult," he wrote in his 1987 essay Not-Knowing, 'but because it wishes to be art."

He is now more referenced than read, but at the time of his death from throat cancer in 1989 Barthelme was, alongside Raymond Carver, the most emulated short story writer in America. The vast majority of his work, unlike that of many of his formally adventurous contemporaries, remains fresh, despite its reputation having been unfairly tarnished by underachieving copyists.

Barthelme's literary antecedents were Stéphane Mallarmé, Joyce, Gertrude Stein, Beckett and the surrealists, although it's true to say that he was equally influenced by the visual arts. He often cited collage as the central artistic principle of the last century and many of his stories work in just such a way, mashing historical and artistic allusions into pop-cultural references and voices that shift between the demotic, the bureaucratic and the formal. Place and time are often elastic or paradoxical. Stories such as City Life (1970) and Will You Tell Me? (1964) are not untypical in having something of the quality of a film watched in fast forward, the familiar connective tissue of plot and commentary almost entirely jettisoned. Elsewhere, in Cortés and Montezuma we find accurate period detail coexisting with detectives and limousines. These last are "only a way of making you see chariots or palanquins", said Barthelme, the comment indicative of the way in which his playfulness is rarely that alone.

Perhaps the most immediately appealing aspect of Barthelme's craft, other than what George Saunders calls "the devastating adroitness of his language", is his supreme talent for comedy. This subsists even in his angriest stories, such as The Rise of Capitalism (1972). Despite noting that his urge to crack jokes was something he developed greater control over as he grew in experience, the high value he placed on humour is indicated by an attack he made on nouveau roman writers in his 1964 essay After Joyce. "It is as if French novelists do not know how to play," he writes, concluding that this inability "is the result of a lack of seriousness".

That judgment, as unexpected as it is perspicacious, is typical of Barthelme, whose work repels certain accusations habitually levelled at postmodernism: that it fails to engage with the world or the human condition, eschewing emotional depth in favour of tail-chasing cleverness. One need only read The Indian Uprising (1968), one of his most famous stories, to be disabused of this notion. Ludic, bizarre and partially opaque as it may be, its presiding atmosphere is nevertheless such that it would surprise few readers to learn that it was written at the height of the Vietnam war. Equally, its description of the waterboarding of an enemy combatant shows its concerns can hardly be said to lie solely with events of the past.

"There's nothing more rewarding than a fresh set of problems," Barthelme commented in a 1987 interview. He both celebrated and despaired of them, and his work essentially represents an ongoing investigation into problematic relationships – between the conflicting sides of the self; men and women; races and societies; competing ideologies; nature and technology; high and low culture; language and meaning – and a sustained attempt to carry out this investigation in an original, meaningful way.

"You can't do Beckett all over again, any more than you can do Joyce again," he told Larry McCaffery in 1980. His work clearly bears the influence of both, and of the Eliot of The Waste Land (particularly in the repeated "Fragments are the only forms I trust" refrain of 1968's See The Moon?), but could never be mistaken for theirs. As with all great artists his influences represented territories to strike out from, not havens in which to settle.

Next time: Jane Bowles