The accurate physical simulation of room acoustics is a very complex task. It is known that the human auditory system is limited in its ability to distinguish between subtle differences in the acoustics of a room. This is for example demonstrated by the observation that certain room acoustical parameters can be highly variable on very short distances while the human auditory system seems to be insensitive to the variations in the associated perception of room acoustical attributes. Therefore it seems attractive, to better understand the human auditory perception of room acoustics and to better know what properties of room acoustics are perceptually relevant. This would help to determine how accurate a room-acoustical simulation needs to be, i.e. to sound the same as the real room that is simulated. In this study the influence of the interaural cross-correlation of the early part and the reverberant tail of a binaural room impulse response on spatial perception is surveyed by directly manipulating the impulse response. The subjective results are compared to the prediction by an auditory model. A two-stage binaural psychoacoustic model is presented, to predict the perception of the acoustics of a room. The first stage extracts the binaural cues and is based on the limits of spatial perception. The just noticeable differences of the interaural cross correlation is used to tune the model. The second stage predicts several perceptual attributes which characterize the perception of room acoustical attributes. The model uses the information of binaural room impulse responses for the prediction of the apparent width of sources and the perceived listener envelopment.