We present a framework for interactive lighting design based on linear re-rendering. The rendering operation is linear with respect to light sources, assuming a fixed scene and camera geometry. This linearity means that a scene may be interactively re-rendered via linear combination of a set of basis images, each rendered under a particular basis light. We focus on choosing and designing a suitable set of basis lights. We provide examples of bases that allow 1) interactive adjustment of a spotlight direction, 2) interactive adjustment of the position of an area light, and 3) a combination in which light sources are adjusted in both position and direction. We discuss a method for reducing the size of the basis using principal components analysis in the image domain.