An LED module that includes an LED (light-emitting diode) (1) and a rotationally symmetrical, bowl-shaped collimator lens (2) is provided. The collimator lens has an inner refractive wall (9), an outer reflective wall (7), a first surface (8) having an entrance aperture (3) with a recess (4) in which the LED is situated and which collimator lens is also provided with a second surface (10) from which light generated by the LED emerges, the normal to the surface extending substantially parallel to the axis of symmetry of the lens, and the LED module also includes one or more of the following structures : (1) a conic wall portion of the recess (4) of the inner refractive wall (9) at the entrance aperture (3) that includes a curved portion (9'), and an outer reflective wall (7) so configured in accordance with the structure of the inner refractive wall (9) to achieve substantial collimation of a source of light (1) at the entrance aperture; and/or (2) a first surface (8) of the lens (2) that is recessed away from the LED source (1); and/or (3) two surfaces (8), (11) of said refractive wall (9) between which the refractive function of said refractive wall (9) is divided. The LED module offers an improvement in the performance of the Flat top Tulip Collimator known in terms of reduced size, beam divergence, beam uniformity, and to some degree efficiency. Moreover, it allows a wider variety of choices in optimizing various performance characteristics, and this in turn allows more flexibility in the structure design.