A method and apparatus for conditioning ambient air for use in an enclosure is disclosed which cools the ambient supply air stream in sensible energy recovery device or cools and dehumidifies the ambient supply air stream in an enthalpy energy recovery device. The thus cooled air is then cooled by a cooling coil of a refrigerant cooling system to reduce its temperature and humidity. The thus cooled and dehumidified air is then passed through a segment of a rotating desiccant wheel or through a different type of desiccant dehumidification device under conditions which reduce its moisture content and increases its temperature.