The binaural interaction component (BIC) of the auditory evoked potential is the difference between the waveforms of the binaural response and the sum of left and right monaural responses. This investigation examined BICs of the auditory brainstem (ABR) and middle-latency (MLR) responses concerning three objectives: 1) the level of the auditory system at which low-frequency dominance in BIC amplitudes begins when the binaural temporal fine structure is more influential with lower- than higher-frequency content; 2) how BICs vary as a function of frequency and lateralization predictability, as could relate to the improved lateralization of high-frequency sounds; 3) how attention affects BICs. Sixteen right-handed participants were presented with either low-passed (< 1000 Hz) or high-passed (> 2000 Hz) clicks at 30 dB SL with a 38 dB (A) masking noise, at a stimulus onset asynchrony of 180 ms. Further, this repeated-measures design manipulated stimulus presentation (binaural, left monaural, right monaural), lateralization predictability (unpredictable, predictable), and attended modality (either auditory or visual). For the objectives, respectively, the results were: 1) whereas low-frequency dominance in BIC amplitudes began during, and continued after, the Na-BIC, binaural (center) as well as summed monaural (left and right) amplitudes revealed low-frequency dominance only after the Na wave; 2) with a predictable position that was fixed, no BIC exhibited equivalent amplitudes between low- and high-passed clicks; 3) whether clicks were low- or high-passed, selective attention affected the ABR-BIC yet not MLR-BICs. These findings indicate that low-frequency dominance in lateralization begins at the Na latency, being independent of the efferent cortico-collicular pathway's influence.