A headlight is disclosed, having separate low-beam and high beam housings. The high-beam housing includes four planar inward-facing reflectors, in the shape of a pyramid, with the high-beam LED array at the apex and a plano-convex high-beam lens at the base. The low-beam housing includes three planar inward-facing reflectors along the top and lateral sides, similarly arranged as three sides of a pyramid. The low-beam housing has one or more planar, horizontal upward-facing reflectors, disposed below the longitudinal axis of the low-beam housing. Light propagating downward from the low-beam LED array directly strikes either the incident face of the low-beam lens or exactly one upward-facing reflector. When viewed from the front of the low-beam housing, the upward-facing reflectors resemble steps that descend from a lower edge of the low-beam LED array.