To examine the independent contribution of various stimulus characteristics to positional judgements, we measured vernier alignment performance for three types of Gabor stimuli. In one, only the contrast envelope of the upper and lower stimulus elements was offset, with the luminance-modulated carrier grating remaining in alignment. In the second, only the carrier grating was offset. In the third, both carrier and envelope were offset together. Performance was examined over a range of element separations. When both cues are available, thresholds for small separations are dominated by carrier offset information and are inversely proportional to carrier frequency. At large separations, thresholds are governed by the spatial scale characteristics of the envelope. For broad-band stimuli such as lines, bars or dots typically used for vernier acuity, their higher frequency content can be used when separations are small, but as separation increases a smooth transition between the scales that determine threshold results in the continuum known as Weber's law for position. That is, with increasing separation, larger scales must be used, and thresholds increase in direct proportion to 1/frequency.