We introduce a new formulation of the lightness problem for images of artworks, such as paintings or frescoes. As artists often paint the effects of light, the albedo field can contain a component that mimics an illumination field. Therefore, new insights are needed to distinguish the effects of physical illumination and painted shading. Because paint has a small dynamic range compared to light, these two signals can be distinguished using dynamic range. We describe a variational method to estimate the physical illumination component. We show our method produces estimates of the illumination intensity field for multispectral images of works of art that compare very well with ground truth, which is known. Our method outperforms other state-of-the art lightness recovery algorithms. For (R,G,B) images of frescoes found on the web, where ground truth is not known, our method produces results that appear to be very good, too.