The luminance of a test within an inhomogeneous ("checkerboard") surround was adjusted to match the brightness of a comparison patch within a uniform surround. All stimuli were achromatic. Both surrounds had the same space-averaged luminance. With an incremental comparison patch, a test-within-checkerboard at a luminance between the luminances of the brighter and dimmer checks appears dimmer than if viewed within the uniform surround. A decremental comparison patch, however, is matched by a test luminance that is little affected by the inhomogeneity of the surround. In general, the brightness of the test is mediated neither by the space-averaged luminance of an inhomogeneous surround, nor by any equivalent uniform surround, regardless of luminance. We consider alternative models for the brightness of a region that is neither strictly an increment nor decrement with respect to contiguous surrounding surfaces.