Tightly focused spots with small central lobes, high central intensity and low sidelobe intensity are desirable for many light-emitting diode based micro-projection system applications. Diffractive optical elements (DOEs) offer a potentially low cost and flexible choice for realizing this task. We have approached the design of suitable elements using two methods: various step size simulated quenching (VSSQ) and multiresolution various step size simulated quenching followed by direct binary search (M-VSSQ-DBS). M-VSSQ-DBS greatly increases the central intensity of the spots, and only slightly influences the sidelobe intensity, most often favourably reducing it. When the central lobe size is 0.8 times that of the geometrical-optics limit, the peak intensity can be as high as 97.73% that of the geometrical spot, and the relative maximum sidelobe intensity is 51.14% of the peak intensity. The designs are tolerant to variations in the actual width of the light source and to lateral misalignment. We verify the designed DOE using rigorous diffraction theory, i.e. the finite-difference time-domain method. The results obtained by scalar and rigorous diffraction theory are in excellent agreement with each other. © 2008 IOP Publishing Ltd.