Flora Belle Buckman, aged ten, is a self-professed "cynic." The daughter of divorced parents, Phyllis (a romance novelist) and George (an accountant), she lives with her mother, and misses her father. She reads comics, including the Amazing Incandesto, a superhero comic, which she enjoys reading with her father. Looking out of her window one day, she sees her neighbour, Tootie Tickham, chasing a runaway vacuum cleaner, the Ulysses 2000, which swallows up a passing squirrel. Flora rushes to the squirrel’s rescue, giving it mouth-to-mouth resuscitation, and taking it home to recover. The squirrel, soon named Ulysses, is transformed by its accident, loving Flora deeply, and becoming a poet, inspired perhaps by a book of poetry belonging to Tootie, which has also been sucked up by the vacuum cleaner. Flora’s mother, Phyllis, dislikes Ulysses, believing him to be dirty and dangerous, and thus begins a battle of wits in which Phyllis tries to have Ulysses killed, and Flora works to rescue him. Along the way, Flora and Ulysses spend time with her father, George, a sad accountant who is devastated by the divorce and loss of time with his daughter. Ulysses, perpetually hungry, causes mayhem in a local doughnut shop, and narrowly escapes being killed by a knife-wielding chef. George takes Flora and Ulysses to his apartment building, where they face a fresh danger in the form of the landlord’s cat, and spend time with George’s neighbour, Dr Meescham. She is a philosopher from a country named Blundermeecen, and offers a number of philosophical insights into Flora’s situation and her relationship with her father. Flora begins to realise that her father loves her, and her cynicism starts to melt a little.
Meanwhile, Tootie Tickham has a visit from her great-nephew, William Spiver, who has been sent to stay by his mother, for an unspecified reason. William and Flora gradually become friends, talking about the meaning of life and the universe, and bonding over being children in divorced families. Eventually they band together to help save Ulysses from Phyllis. William claims to be blind, following a traumatic event – it emerges he had pushed his stepfather’s truck into a pond, and been banished from the house by his mother. The novel ends with William able to remove his dark glasses and see, and Flora, a cynic no longer, reconciled with her mother, and seated on Dr Meescham’s couch, surrounded by her parents and her new friends. She has hope for the future.