A white light source includes a short wavelength LED and a phosphor layer that emits light at longer visible wavelengths. A dichroic reflector transmits the longer wavelength light, and reflects some LED light onto the phosphor such that as light travels from the LED to the dichroic reflector it does not pass through the phosphor. The LED may emit blue light, and the dichroic reflector may transmit a second portion of the LED light, such that the light source output light includes both the second portion of the LED light and the longer wavelength phosphor light. The LED may be mounted on a flexible substrate having a cavity region and neighboring region, the LED being mounted in the cavity region. A dielectric layer may be thinner in the cavity region than in the neighboring region, or a hole may extend completely through the dielectric layer in the cavity region.