An array of LEDs is supported by a support mechanism that both supports conductors leading to the LEDs and sinks heat from the LEDs. The support mechanism may be a transparent heat-conducting sheet or an array of cantilevered arms at different angles that support the LEDs and sink heat. This reduces the blockage of light. The LEDs are positioned generally in the focal plane of an array of concave mirrors that collimate the light. The LEDs and array of mirrors are translatable with respect to one another to steer the aggregate light beam to customize the emission. In another embodiment, multiple LEDs are positioned over each mirror in the mirror array, and the combination of LEDs illuminated over each mirror is used to steer the aggregate light beam from the luminaire.