The visual system's computation of lightness (perceived reflectance) leads to contrast effects in which a gray target region appears lighter on a black background than on a white one. Here we show a paradoxical contrast effect in which targets look lighter after adding regions that increase the scene's average luminance, and darker after adding regions that decrease this luminance. The paradoxical effect emerges if the target sits either on a black local background surrounded by a white remote background, or on a white local background surrounded by a black remote background. It does not occur if both backgrounds have the same luminance. The effect is consistent with Bressan's double-anchoring theory, and likely also with those edge-integration theories that assume gain control, but differs from previously reported effects of assimilation, articulation, reverse contrast, and remote contrast.