Presented is an LED device that produces white light by performing phosphor conversion on substantially all of the primary light emitted by the light emitting structure of the LED device. The LED device comprises a light emitting structure and at least one phosphor-converting element located to receive and absorb substantially all of the primary light. The phosphor-converting element emits secondary light at second and third wavelengths that combine to produce white light. Some embodiments include an additional phosphor-converting element, which receives light from a phosphor-converting element and emits light at a fourth wavelength. In the embodiments including an additional phosphor-converting element, the second, third, and fourth wavelengths combine to produce white light. Each phosphor-converting element includes at least one host material doped with at least one dopant. The phosphor-converting element may be a phosphor thin film, a substrate for the light emitting structure, or a phosphor powder layer.