Generating clones of mutated cells within a wild-type tissue is a powerful experimental paradigm for elucidating gene function. Recently, this approach was employed for identifying genes that shape morphogen profiles in the Drosophila wing-imaginal disc. Interpreting such experiments poses a theoretical challenge. We present a general framework that links specific features of the morphogen profile in the clone vicinity to three basic morphogen properties: diffusion, degradation, and binding to immobile elements. Our results provide rigorous criteria to examine existing data and can facilitate the design and interpretation of future clone experiments.