A Shih-Poo is a Poodle hybrid that is a cross-breed of a Poodle and a Shih-Tzu and may demonstrate any combination of traits from those two breeds. Poodle hybrids have become very popular in the past few years. They play a big role in the current designer dog trend. The cross with the Poodle is usually because of the Poodle's non-shedding coat.