White's effect is a phenomenon in which grey bars replacing segments of the white phase of a square-wave grating appear darker than those replacing segments of the black phase. The direction of the brightness difference is consistent with brightness assimilation rather than with brightness contrast. We present data from two experiments which measure the degree of the brightness difference in stimuli consisting of just three inducing bars and a single grey test bar, as a function of various spatial manipulations of the inducing and test bars. The spatial manipulations were chosen to maximise the opportunity for assimilation effects to manifest themselves. The results do not support the view that assimilation is an important component of the effect. The data are shown to be consistent with our model of brightness induction in which both a local and a more spatially extensive contrast mechanism operate to produce White's effect.