Top 10 Non-Shedding Dog Breeds By Staff Writer - Sep 5, 2014 24044 Share on Facebook Tweet on Twitter tweet Havanese Another good choice for families with children, the Havanese is friendly and spirited. One caveat, the Havanese requires nearly constant human companionship, making it unsuitable for those who are away from home a lot. Havanese: Image -Thinkstock PREV9 of 11NEXT