A classical objective measure for binaural fusion at the brainstem level is the so-called β-wave of the binaural interaction component (BIC) in the auditory brainstem response (ABR). However, in some cases it appeared that a reliable detection of this component still remains a challenge. In this study, we investigate the wavelet phase synchronization stability (WPSS) of ABR data for the analysis of binaural fusion and compare it to the BIC. In particular, we examine the impact of monaural nonlinear frequency compression on binaural fusion. As the auditory system is tonotopically organized, an interaural frequency mismatch caused by monaural frequency compression could negatively effect binaural fusion. In this study, only few subjects showed a detectable β-wave and in most cases only for low ITDs. However, we present a novel objective measure for binaural fusion that outperforms the current state-of-the-art technique (BIC): the WPSS analysis showed a significant difference between the phase stability of the sum of the monaurally evoked responses and the phase stability of the binaurally evoked ABR. This difference could be an indicator for binaural fusion in the brainstem. Furthermore, we observed that monaural frequency compression could indeed effect binaural fusion, as the WPSS results for this condition vary strongly from the results obtained without frequency compression.