A numerical study is conducted concerning the improvement of radial plane fins heat sinks for natural convection cooling of light-emitting diode (LED) lamps. The main objective is to maintain the temperature of the heat sink base below a prescribed threshold for a given released heat flux at the heat sink, minimizing its mass and maintaining at a reasonably simple level the manufacturing processes and operations required for its production. Starting from a previously optimized heat sink for the same purpose, constituted by complete rectangular radial plane fins, the present study aims at further improvements by considering incomplete rectangular radial plane fins. The main objective of this study is to find the best profile for the turning operation to obtain the radial plane fins lighter configuration. It is found that this can be achieved by removing part of the upper internal corners of the rectangular fins, more specifically shaping a curved cut, leading to heat sink mass reduction up to 32.4%. The geometry of the improved heat sink is of cylindrical nature, obtained from cutting an aluminum extruded bar comprising a cylindrical central core and a number of uniformly distributed rectangular radial plane fins, followed by a simple turning operation to remove their upper internal corners. Even if results concern a particular LED lamp, the main ideas and approach prevail to improve other types of heat sinks for general light and/or electronic components cooling.