African pygmy hedgehog
There are no two words that sound cuter together than pygmy and hedgehog. As it says on the tin, these are domesticated miniature hedgehogs – and you can expect them to live for up to 10 years. Make sure you’re fully aware of the ethical issues before purchasing.
Bearded dragon
Possibly the most fierce sounding of pets, the bearded dragon isn’t actually a fire-breathing reptile, but a popular choice of lizard for people who want a little companionship. Once your scaly sidekick is comfortable in its new environment, they’re quite happy to be handled and may even sit on your knee or shoulder.
Fish
There are so many different kinds of fish you can keep, from common goldfish to tropical tetras and swordtails, that these low-maintenance little critters can suit every budget. You can mix and match your fish too – and enjoy a rainbow of colours swimming around in your tank.
Sugar glider
One of the more unusual choices of pet, the exotic sugar glider is a short-haired marsupial, known for being sociable and cuddly when domesticated. The name refers to their natural diet of nectar and the flap of skin between their wrists and ankles that allows them to glide when jumping from tree to tree.
Sugar gliders are very sociable animals, and best kept in pairs. Note that keeping Sugar gliders as pets is actually illegal in some countries.
Talking parrot
If you’re after interaction, you might get more than you bargained for with a talking parrot. They come in all shapes, colours and sizes, so whether you go for the African Grey – considered to be one of the most intelligent birds in the animal kingdom – or a simple budgerigar, which will mimic songs and phrases, there’s a parrot for every taste.
Pot-bellied pig
If you’re looking for something with intelligence, personality and charm, a pot-bellied pig might be ideal. As long as you’ve enough time and space, these chubby characters make for rewarding pets: they’re non-allergenic, affectionate and, surprisingly, usually odour-free.
Tortoise
You won’t be taking it for a brisk daily walk, but a tortoise can certainly bring you some sneeze-free fun. There are a few different types of these shell-dwelling reptiles to consider in a variety of sizes – some won’t grow larger than the palm of your hand, while others will reach the size of a football.
Corn snake
Great pets for adults and kids, corn snakes are easy to handle and relatively simple to care for. If you can get past the initial unease of feeding them small rodents for lunch, they can be friendly, inquisitive and interesting pets to keep.
Stick insect
Probably the lowest-maintenance pet there is, stick insects require very little care beyond ensuring they have a tank and the right edible plant. As the name suggests, they look much like small sticks and branches – and while they may not be the most exciting of companions, you can’t play spot the stick insect without them.
Always take expert advice before adding any pet to your household, especially exotic animals.
Please note, Direct Line Pet Insurance only covers cats and dogs.
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This article was amended on 1 April 2015 to refine advice on Sugar Gliders