A steerable illumination fixtures include an emitting source and a refractive optical system that steers an emitted beam by relative translation of the emitting source against the optical system. The light emitting source may be placed along an optical axis of one or more lenses to produce an output beam along that axis, or translated in-plane (orthogonal to the optical axis) relative to the lenses to produce a steered beam. The optical system may include refractive lenses and in some embodiments mixing channels and/or one or more baffles with apertures. The design is typically optimized to produce a round, uniform beam that retains approximately the same power level and beam width as it is steered. It is beneficial, but not required, that a second lens have a diameter equal to or larger than a first lens. The lenses may be configured so that the effective focal plane of the two lenses together is located approximately at the plane of the light emitting source.