Recently the influence of delay and azimuth of a single speech reflection on speech reception thresholds (SRTs) was systematically investigated using frontal, diffuse, and lateral noise [Warzybok et al. (2013). J. Acoust. Soc. Am. 133, 269-282]. The experiments showed that the benefit of an early reflection was independent of its azimuth and mostly independent of noise type, but that the detrimental effect of a late reflection depended on its direction relative to the noise. This study tests if different extensions of a binaural speech intelligibility model can predict these data. The extensions differ in the order in which binaural processing and temporal integration of early reflections take place. Models employing a correction for the detrimental effects of reverberation on speech intelligibility after performing the binaural processing predict SRTs in symmetric masking conditions (frontal, diffuse), but cannot predict the measured interaction of temporal and spatial integration. In contrast, a model extension accounting for the distinction between useful and detrimental reflections before the binaural processing stage predicts the data with an overall R(2) of 0.95. This indicates that any model framework predicting speech intelligibility in rooms should incorporate an interaction between binaural and temporal integration of reflections at a comparatively early stage.