This study examines how judgments of a region's contrast are influenced by components of a heterogeneous surround. Each stimulus comprised a 5x5 grid of squares in a homogeneous background of fixed mean luminance, with the central square the target. On a given trial, the task was to judge (with feedback) whether the (Weber) contrast of the target was 0.04 or -0.04 (relative to the background); the contrasts assigned (in random order) to the 24 surrounding squares were drawn from the values -0.98, -0.33, 0.33, 0.98 in conformity to one of nine pre-chosen histograms. Presentations were brief (80 ms) in one condition and long (800 ms) in another. A novel psychophysical method was used to estimate the impact exerted on judged target contrast (JTC) by a given contrast in a given grid position. Results were similar for four observers. For both display durations, the four squares sharing an edge with the target influenced JTC 2.4-9 times more than any other surrounding squares. In long presentations, abutting squares of extreme contrast repelled target contrast: squares of contrast -0.98 (0.98) increased (decreased) JTC. However, lower contrast abutting squares attracted target contrast: squares of contrast -0.33 (0.33) decreased (increased) JTC. This central finding can be explained by supposing that: (a) JTC is strongly correlated with the average boundary contrast from surround to target, as registered by linear, edge-selective neurons, and, crucially, (b) the responses of these neurons are themselves subject to lateral inhibition from the rectified responses of other similarly tuned neurons. Finally, in brief presentations, a polarity-specific asymmetry was observed: the two positive abutting-square contrasts continued to influence JTC as they did in long presentations, but contrasts -0.33 and -0.98 ceased to exert much impact, suggesting that lateral influences on target appearance propagate more quickly from positive than from negative contrast abutting regions.