Edward is a state-of-the-art antihero: afraid of everything and unequal to every challenge. He’s there to remind us that we all grow at our own pace, that nobody should judge us when we fail, that there’s always cinnamon toast. Edward’s also a patron saint for this season’s children’s books, which have been thick with underdogs (and undercats). Unlike Edward, most manage to triumph in the end–to escape the pot of boiling water, to thwart the Emperor or overcome straight hair–but let’s not hold that against them. Their stories are all comforting–and set down with tremendous sympathy. In the jacket copy for How Emily Blair Got Her Fabulous Hair (Bridgewater. $14.95), Susan Garrison explains her bond with her curl-challenged heroine: “I had my first Tonette home permanent by age six and am still striving for total hair confidence ? (“Emily” was illustrated by Marjorie Priceman. Her work, an uninhibited blend of Bemelmans and early Warhol, also bounds through Zin! Zin! Zin! A Violin [Simon & Schuster. $15].) Care to meet more underdogs? Here we go, unready or not.

Two books that caught (and held) our eye this year concern man-made disasters: oilspills and math. Washing the Willow Tree Loon (Simon & Schuster. $16) is about a bird who has crossed paths with a leaking barge. Jacqueline Briggs Martin’s prose is light on politically correct pomp and Nancy Carpenter’s oil paintings are so lovely and still they sort of echo. Who’d have thought somebody could do an oil-spill book without sliming us? Math Curse (Viking. $16.99) is an altogether, uh, loonier book. It’s the latest collaboration from the fabulously bratty team of writer Jon Scieszka and illustrator Lane Smith and concerns a young girl who’s been unhinged by Mrs. Fibonacci’s math class. She and her classmates have a miserable time trying to divide 24 cupcakes among 25 people, but then our heroine has a flash of genius and raises her hand: “I’m allergic to cupcakes.”

After the anarchic “Math Curse,” your eyes will need a holiday, so take in the simple pleasures of Maisy’s Pop-up Playhouse (Candlewick. $17.95). Lucy Cousins’s mouse has a cute bellybutton–plus, she’s Edward the Unready’s spiritual kin. She loves her creature comforts. And, if you’ve already read “Maisy Goes to the Playground” or “Maisy Goes to Bed,” you know she’s not exactly an overachiever. “Playhouse” is a bright piece of work that blooms in your hands when you open it. You’ll find Maisy in the shower apparently, she wasn’t expecting company. (For further adventures in 3-D, try David Pelham’s The Sensational Samburger. It’s a good gross-out: a cardboard sandwich crawling with bugs and worms [Dutton. $12.99].)

Often, all an underdog needs is a shot of self-esteem. In David Shannon’s The Amazing Christmas Extravangza (Blue Sky. $15.95), Mr. Merriweather is nonplusseal when a neighbor criticizes the holiday decorations on his house: “Kind of a shrimpy little string of lights ya got there, pal.” Before long, he’s turned his modest cottage into a monument to Christmas kitsch that sparks a neighborhood riot. In Joan Rankin’s The Little Cat and the Greedy Old Woman (McElderry. $16), a hungry tabby becomes so enraged with his parsimonious mistress that he grows to a hundred times his normal size and terrorizes her. (Rankin painted her terrific watercolor illustrations on damp paper so the cat is literally blurry with rage.) Elsewhere, our put-upon heroes settle for modest victories. Writer Jim Latimer and illustrator Tom Curry’s charming Snail and Buffalo (Orchard. $14.95) is a variation on the unlikely-friendship story: a snail with a self-image problem wins a buffalo’s respect by showing him how she can whorl, siphon and retract. The Reverend Thomas’s False Teeth (Bridgewater. $14.95) is a folk tale, retold by Gayle Gillerlain, about a young black gift who can’t get her family’s attention until she solves the dilemma of the day: fishing the preacher’s dentures out of the bottle-strewn Chesapeake Bay. Reverend Thomas thanks Gracie kindly, then slides his teeth back into his mouth. Sweet story–and Dena Sehutzer’s loose, gestural paintings are glowing with life–but maybe the preacher should have run those things under the faucet?

Folk tales are rife with underdogs, of course. In The Rabbit’s Escape (Holt. $15.95), our hero is duped into visiting the bottom of the sea, where an ailing Emperor plans to snatch his liver for a cure. Quick on his feet, the rabbit insists he doesn’t have his liver with him. Do you love it? Suzanne Crowder Hah retells the story in Korean and stately English: “‘Turtle,” the Dragon King finally spoke, ’take the rabbit to get his liver’.” And Yumi Heo offers gorgeous paint-and-pencil illustrations that are flat and spindly like cave paintings. Mediopollito/Half-Chicken (Doubleday. $15.95) is a Spanish-and-English retelling of a folk tale about the origin of the weathervane. Writer Alma Flor Ada and illustrator Kim Howard give us a chicken with one eye, one leg and one wing. Talk about an underdog. The chicken sets out for Mexico City, befriending fire, water and wind along the way. Later, when the Palace chef dumps him in the soup, his buddies conspire to save him. The water puts out the fire. The wind carries him away.

Nice to have friends. And nice, as a reader, to have a cool creature to root for. What’s great about underdog books is that they’re out to make you feel good, not bad. They’re not wagging their finger at you like those stories about how pride goeth before a fall. Cat, You Better Come Home (Viking. $15.99) is the tale of an uppity prodigal pet who dumps her owner for the international high life and changes her name from Puff to Clarice. Steve Johnson and Lou Faneher’s paintings have a playful elegance, but Garrison Keillor’s verse may be too clever and Cole Portery for some kids. (You can imagine Keillor singing it aloud, which you might not consider a plus.) The real trouble, though, is that you’re not rooting for anybody. You’re dying for the cat to get what’s coming, and she does: she winds up dragging home so fat and ragged she looks like some debauched Gabor sister. There’s no fun in that. OK, maybe a little. But next time give us a hero, not an enemy.

One hero, coming up. Eric Carle’s The Very Lonely Firefly (Philomel. $19.95) is the fourth installment in his “Very Quartet,” which has been in the making since 1969. In the jacket copy, he says he wanted each book to be about one thing. “The Very Hungry Caterpillar”? Hope. “The Very Busy Spider”? Work. “The Very Quiet Cricket”? Love. And “The Firefly”? Belonging. These are roughly the stages of life–with “belonging” being Carle’s euphemism for death. “The Firefly” ends with the main character coming, at long last, upon others of his kind: a sky full of fireflies, whose tails are actually flashing off and on, thanks to a cell battery in the book. (We know a metaphor for the migration of souls when we see one. What are we, children?) It’s a nice moment, and it gets at the heart of all this underdog business. All anybody wants to know is that–no matter how bad their math, how straight their hair–they’re not alone. And they’re not, of course. Anyone for cinnamon toast?