FEARLESSNESS IS ONE OF those characteristics that you either have from the start, or don’t. The sort of child who will pick up a spider, or go to sleep without worrying what might be under the bed is not always deficient in imagination – nor necessarily the product of robust parenting.

If you have at least one small child who needs regular doses of reassurance, then Emily Gravett’s Little Mouse’s Big Book of Fears is for you. “Living with fear can make even the bravest person feel small,” it says, before going on to describe most of those that plague children – though not, as it happens, those of losing a parent – through death or divorce – or of predatory paedophiles.

One of the most interesting new picture-books to have emerged in the past two years, Gravett’s Wolves and Meerkat Mail displayed a fluid, quirky draughtsmanship that was instantly appealing. This, though, has the quality of great picture-books such as those by Allan and Janet Ahlberg. It uses the idea of a mouse nibbling through a book to highlight, tease and encourage children into confronting their fears.

Other books are aimed at this market, from Jeanne Willis’s The Monster Bed to Ed Emberley’s Go Away Big Green Monster, but Gravett’s is more creative because Little Mouse is also clearly the artist – drawing the spider’s web, the monsters under the bed, the sharp knives (used in the Three Blind Mice) and wincing away from one completely black page representing the dark. The exquisitely expressive mouse admits “I’m afraid of nearly EVERYTHING I see,” before adding with a grin: “But even though I’m very small . . . she’s afraid of ME.” The “she” is represented by a pair of large, bare feet standing on a chair.

Collage, cutouts and folding flaps are relatively familiar features of a certain kind of picture-book, and too often these are used overlavishly. Gravett’s appear as the product of a stunning visual imagination. My own favourite was a series of time-lapse “Polaroids” of the mouse as it gets sucked down the plug-hole, but my son loved the “Isle of Fright” map, with such geographical features as Shaking Point and Mount Apprehension. It’s simple enough for a toddler of 2+ to understand, but sophisticated enough for an 11-year-old to enjoy. Bravo!

Julia Donaldson’s Tyrannosaurus Drip is about quite another kind of response to fear. Our hero is stolen as an egg. A vegetarian duckbill dinosaur, he hatches out in a family of scowling, growling T-Rexes. “And they shouted, ‘Up with hunting’ and they shouted, ‘Up with war!’/ And they shouted, ‘Up with bellyfuls of duckbill dinosaur!’ ” Donaldson is always fascinated by opposites meeting and failing to understand their differences, and this irresistible tale is almost as good as her masterpiece, The Gruffalo. The pictures by David Roberts have an elegant, satirical line that is most entertaining. His bright red Tyrannosaurus family looks as glum as Gordon Brown; the smooth blue Compsognathus who steals our hero for her own babies to eat could be David Cameron, and the serene rotundity of the duckbills, with their closed eyes and stuck-up noses, well, they remind me of children who come to tea and announce their preferences much as Drip does: “And he said, ‘I’m really sorry,’/ and he said, ‘I simply can’t’./ And he said, ‘This meat looks horrible./ I’d rather eat a plant.’ ” Much as I adore this book, I’m afraid my own heart is with the beastly but lively T-Rex families. They are defeated, of course, by fear of their own reflections.

Little Mouse’s Big Book of Fears by Emily Gravett

Macmillan, £12.99; 32pp

Buy the book here for the offer price of £11.69 (free p&p)

Tyrannosaurus Drip by Julia Donaldson

Macmillan, £10.99; 32pp

Buy the book here for the offer price of £9.89 (free p&p)

Times Recommends

• Superfreakonomics by Steven D Levitt and Stephen J Dubner
• The Times picks the 50 best paperbacks of 2009
• Vincent van Gogh’s letters show the soul of the artist