A survey of data on the perception of binaurally presented sounds indicates that loudness summation across ears is less than perfect; a diotic sound is less than twice as loud as the same sound presented monaurally. The loudness model proposed by Moore et al. [J. Audio Eng. Soc. 45, 224–240 (1997)] determines the loudness of binaural stimuli by a simple summation of loudness across ears. It is described here how the model can be modified so as to give more accurate predictions of the loudness of binaurally presented sounds, including cases where the sounds at the two ears differ in level, frequency or both. The modification is based on the idea that there are inhibitory interactions between the internal representations of the signals at the two ears, such that a signal at the left ear inhibits (reduces) the loudness evoked by a signal at the right ear, and vice versa. The inhibition is assumed to spread across frequency channels. The modified model gives reasonably accurate predictions of a variety of data on the loudness of binaural stimuli, including data obtained using loudness scaling and loudness matching procedures.