Sixteen children were given four successive circle-size discrimination problems with luminance as the fading stimulus. Children who were first presented with a difficult size discrimination failed to acquire this discrimination. Those who first received an easy discrimination learned the difficult discrimination. At the end of each 10-trial block, two probe stimuli were presented to monitor any shift in control from luminance to size. One probe was the same size as the positive stimulus but of different luminance; the other was the same luminance but of different size. If, in the course of fading, size and luminance both controlled responding, fading was successful. If luminance alone controlled responding until the end of fading, the size discrimination was not established. Dual control, and thus successful fading, resulted when the target stimuli were very discriminable, or when the target stimuli were subtly different provided that previous fading series had first established less subtle discriminations.