Experimental results are described for the dependence on interaural stimulus parameters of subjective lateral‐position matches and just‐noticeable differences (jnd’s) in interaural amplitude and time. All experiments employed 500‐Hz tones presented through acoustically monitored headphones. The overall amplitudes of the stimuli were iteratively adjusted to eliminate subjective loudness cues in the interaural‐amplitude jnd experiments. Performance in the experiments is analyzed within the framework of a probabilistic lateralization model in which internal noise is explicitly treated. The model predicts a specific relation between position matches and the interaural amplitude and time jnd’s. The data are qualitatively consistent with the predictions, and the quantitative agreement is good for one subject, moderate for the second, and poor for the third. In particular, the model predicts the observed asymmetry in the dependence of the interaural‐time jnd on interaural time delay for nonunity interaural amplitude ratios. Calculated values of the internal noise of the subjective image position are in qualitative agreement with reports by observers of image diffuseness as a function of interaural parameters of the stimulus.