In dogs, you could consider Schnauzers, short-haired terriers, greyhounds, poodles, Bichon Frises, Maltese, Basenji (cute) - they hardly shed. In cats, Abyssinians, Burmese, Tonkinese, Korat. Once they are in your house, vacuum carpets, curtains & upholstery often. Laminate floors are better, but downfall is that the pet could scratch them or slide to their oblivion! Clean out litter trays regularly (more so than advised). Restrict the pet from bedrooms where the asthmatic sleeps. Also, avoid wearing garments (i.e.: fluffy slippers) that pick up and carry dander around the house.