Disclosed herein are apparatus, methods, and systems for deriving composite beams from a plurality of light sources such as LEDs. Optical units comprising a plurality of light sources, each source having an associated optic which is individually positionable, are developed using optimization techniques that allow for lighting different target areas in an effective manner by rotating or otherwise positioning the reflectors, refractive lenses, TIR lenses, or other lens types to create a composite beam. The apparatus, methods, and systems of lighting herein make it possible to widely vary the types of beams from an available fixture using a small number of optics and fixtures. In some cases, by using a combination of individual beam patterns from the same or different types of light sources, a small set of individual optics may be sufficient to create a majority of the typical and specialized composite beams needed to meet the needs of most lighting projects and target areas.