Asthma affects about 4 million children in the United States and is a leading cause of hospitalizations and school absenteeism. Continuous wheezing in very young children may develop into asthma. Low doses of inhaled corticosteroids (ICS) are commonly prescribed to treat children with particularly bad wheezing episodes. This study will compare the safety and effectiveness of low doses of ICS taken daily versus higher doses of ICS taken only during respiratory tract illnesses for toddlers with continuous wheezing or coughing illnesses.