The processing of a visual stimulus is known to be influenced by the statistics in recent visual history and by the stimulus' visual surround. Such contextual influences lead to perceptually salient phenomena, such as the tilt aftereffect and the tilt illusion. Despite much research on the influence of an isolated context, it is not clear how multiple, possibly competing sources of contextual influence interact. Here, 10 using psychophysical methods, we compared the combined influence of multiple contexts to the sum of the isolated context influences. The results showed large deviations from linear additivity for adjacent or overlapping contexts, and remarkably, clear additivity when the contexts were sufficiently segregated.Specifically, for adjacent or overlapping contexts, the combined effect was often lower than the sum of the isolated component effects (sub-additivity), or was more influenced by one component than another 15 (selection). For contexts that were segregated in time (600 ms), the combined effect measured the exact sum of the isolated component effects (in degrees of bias). These results imply that the "encoding" of the context is a compressive non-linear transformation, followed by a non-linear selection, manifested by strong interactions between the encoded components. For selected encoded representations, the contextual influence is a linear sum of the individual effects, as predicted from a theory of optimally 20 combining reference cues.