We ask whether the well known Weber's law between spatial localization and element separation for high contrast, spectrally broad-band stimuli is a consequence of the organization of the early visual filters, or a fundamental constraint on the computation of spatial position by more central mechanisms. We address this question by identifying the individual contributions of mechanisms tuned to different ranges of spatial frequencies and contrast. We measure spatial-alignment and bisection error as a function of element separation at each of a number of spatial scales, using spectrally narrow-band stimuli of fixed supra-threshold contrast. We show that stimuli which minimize the extent of neural recruitment across different spatial channels before the site of extraction of the local contrast energy (and to 2 lesser extent across different contrast channels) do not exhibit Weber's law for either alignment or bisection. We present evidence that Weber's law for localization with increasing separation, found for stimuli of high contrast and broad-band spatial frequency content, is a consequence of the successive disengagement of unitary neural mechanisms, each of which has different spatial and contrast properties, and none of which individually exhibits Weber's law for spatial position.