In a single lighting device including a large number of light-emitting elements (LEEs), the LEEs are divided into separately powered groups, and different combinations of the groups are fully energized to achieve the desired overall brightness. In some embodiments, the number of LEEs in each group has a binary relationship to the other groups. The resolution of the dimming is the brightness of the smallest group. In one example of five binary weighted groups of LEEs, 32 brightness levels can be achieved while the LEEs in the energized groups are fully ON. Thus, since there is no high frequency switching, there is substantially no power dissipation by the dimming control system, and there is limited noise or EMI created. The dimming control can be easily implemented with a logic circuit controlling a transistor switch for each group.