In A Heartbreaking Work of Staggering Genius, Dave Eggers suspected himself of many sins: chiefly that of dishonesty, or rather, the false uses to which honesty might be put. The book is a portrait of the artist with his kid brother, whom he brought up after their parents died of cancer. Mourning involves an enduring relationship to one's sincerity. His style was pre-emptively critical: anything you could doubt about him, he could doubt better. The charm of this lay in the way he doubted his own literary pretensions: "Ooh, look at me, I'm Dave, I'm writing a book! With all my thoughts in it! La la la!" He wrote well, conscious that writing well aligns you with the people you used to mock: grown-ups generally, high-school English teachers in particular. So he made a fuss over themes and foreshadowings - from the back of the class, as it were, of his own work. And he pointedly insisted on describing what he felt like describing, for his own, rather than the book's, sake: how good he is at frisbee, for instance. He deserves to be admired.

In his first novel, You Shall Know Our Velocity, Eggers has grown up in style, though it retains some of its predecessor's irreverence: the story starts on the cover and keeps going; two pages are blank while the motor boat the narrator is standing in skips a wave. But the plot is tighter and Eggers sticks to it. Will and Hand, two friends mourning the death of a third, Jack, set off on a world tour. Will has come into some easy and, as he thinks, shameful money: his silhouette was used in an advertisement, and his cut was $80,000. The friends have only a week to make their trip, and Will plans to give the rest of his money to the poor they encounter. Much of the story involves the crack-up of Will's inner life; this is mirrored by the beating his outside took when somebody Hand had offended took his anger out on Will, who was clearing out Jack's belongings at the time. The incident makes more thematic than structural sense: grief, it seems, demands a kind of retribution for its inadequacy, physical proof of inner suffering.

The simple plot-line allows Eggers to deal practically in hard questions: his heroes have a world to see, a week to do it in, and roughly 40,000 leftover dollars to give away. What's the best way to spend the time and money (or, to put it more grandly, one's life and riches)? The question of where to stop in a week around the world is interesting enough in its own right, besides which it vividly evokes the trivial pursuits of all travellers - their curiosity and gamesmanship - as they endure the delays and repetitions inseparable from any journey. Despite the limitlessness of their ambitions - to see the world, regardless of the price - they spend their days dealing only in limitations. In fact, the strength of the novel lies in just how ordinary their journey is: dull and tiring, occasionally epiphanic, though even the breakthroughs are usually inspired by exhaustion, misunderstandings, or just plain drunkenness. There is no sex but plenty of squalor on the trip.

Giving the money away doesn't prove any easier than getting around the world. Will understands the arrogance of his charity from the first: he chooses whom to bless with money he feels he has no title to. Self-awareness doesn't stop him from being choosy. He finds it hard to give away money in the first place - it is a difficult social gesture, like introducing yourself to strangers at a party - and harder still to give it to grasping people who annoy him.

The novel, like the memoir, deals in the current generational anxieties of the American middle class. Why are we so rich? Why aren't we happier? How can we be less self-centred? Eggers is conscious of the contradictions in all this worrying, and used to thinking in terms of exploitation. Self-doubts are almost always self-serving. Every answer strikes him as the exploitation of a purer question , just as mourning is an exploitation of (someone else's) misfortune. So he tends to hedge his bets, backing sincerity and hypocrisy, optimism and cynicism, all at once. When, towards the end of his trip, Will finally accepts the offer of a prostitute - an older, overweight and unattractive Russian woman, stuck in unwelcoming Latvia - they end up simply keeping each other warm, a human kindness on which Will can no longer put a value.

Prose that consistently undermines itself often leaves nothing but a kind of sentimentality standing at the end. And Eggers's work preaches sentiment, in spite of his carefully constructed embarrassment. His memoir described the "lattice" of fellow-feeling that could hold up drooping humanity. And the novel recommends, in simplest terms, that we live, live, live, as if we were going to die - which, of course, we are. At worst, such sentiments tend towards a bumper-sticker morality, no matter how ironically proclaimed.

The title You Shall Know Our Velocity comes from a lengthy anecdote about a harmless, foolish and ambitious South American tribe who believed they could jump their way to heaven. Its relation to the story is clear, and explains why their failure and nobility appealed to Eggers. On the whole, the novel is tighter, and consequently less evocative, than his first book. But he deserves his success - he writes well and he practises what he preaches: he teaches literacy at his own foundation in San Francisco, while McSweeney's, the independent literary magazine and press that he founded, is now the place publishers look for new talent. A Heartbreaking Work of Staggering Genius reads like the work of a writer who was having fun with literature; there is less fun in You Shall Know Our Velocity, but Eggers is still doing what he likes.