Like poodles, the Bichon frise is a lower-allergen dog. Due to their curled coat, dander stays trapped. These dogs are usually groomed often, which also means that less dander is being released into the air. While allergy sufferers may tolerate this small pet, the Bichon frise can develop a lot of allergies. No matter how well-bred it may be, according to Pets 4 Homes, especially to foods and fleas.