A light source suitable for general lighting applications combines at least one remote phosphor LED and at least one direct emitting LED in a single unit. Both the remote phosphor LED and the direct emitting LED are carried by a base and covered by a bulb or other suitable cover member, which may be light-diffusing. The remote phosphor LED includes a first LED, a phosphor layer, and a first dichroic reflector. Excitation light from the first LED is reflected by the first dichroic reflector onto the phosphor layer to generate phosphor light, which is substantially transmitted by the first dichroic reflector. At least some light from the direct emitting LED propagates to the cover member without passing through any dichroic reflector, including the first dichroic reflector. The light source may provide white light output using relatively small amounts of phosphor material.