Discrimination of the relative spatial phase of sinusoids is reformulated as a local contrast discrimination task. This provides a good account of performance with gratings composed of a fundamental and either its second or fourth harmonic. The contrast of the compounds (including a fundamental and its third harmonic) are then varied, keeping the contrast ratio of the components constant and it is found that performance improves with increasing contrast. The exponent of the power equation relating a base contrast measure to the contrast difference at threshold is derived (assuming the above reformulation to be valid). The average exponent (0.54) is in the range expected from contrast increment detection literature. The effect of contrast on performance is predicted very well. Phase per se does not need to be considered.