Light sources are disclosed utilizing LED dies having at least one emitting surface. An optical element is provided for efficiently extracting light out of an LED die by controlling the angular distribution of the emitted light. The optical element is optically coupled to but is mechanically decoupled from the emitting surface of the LED die. The optical element has an input surface that is optically coupled to the emitting surface, an output surface that is larger in surface area than the input surface, and at least one intermediate surface.