Swan's work has received limited critical attention. Swan published about a dozen stories in various literary magazines across North America and had no books published before she won the 2001 O. Henry Award with her story “The Deep.” Some journals in which her work was published are high caliber publications, such as Harpers and the Ontario Review. “The Deep” was republished in Swan's first book, a collection of short stories, The Deep and Other Stories. This collection was short-listed for the 2003 Commonwealth Writer's Prize “Best First Book” category.

In her introduction to Swan's story in the official O. Henry award volume, Mary Gordon, one of the judges for the 2001 O. Henry Award, commended Swan and “The Deep”:

I chose this story as first among so many strong others because of its utter originality, its daring to assert the primacy of complexity and mystery, its avoidance of the...