Sounds emitted by different sources arrive at our ears as a mixture that must be disentangled before meaningful information can be retrieved. It is still a matter of debate whether this decomposition happens automatically or requires the listener's attention. These opposite positions partly stem from different methodological approaches to the problem. We propose an integrative approach that combines the logic of previous measurements targeting either auditory stream segregation (interpreting a mixture as coming from two separate sources) or integration (interpreting a mixture as originating from only one source). By means of combined behavioral and event-related potential (ERP) measures, our paradigm has the potential to measure stream segregation and integration at the same time, providing the opportunity to obtain positive evidence of either one. This reduces the reliance on zero findings (i.e., the occurrence of stream integration in a given condition can be demonstrated directly, rather than indirectly based on the absence of empirical evidence for stream segregation, and vice versa). With this two-way approach, we systematically manipulate attention devoted to the auditory stimuli (by varying their task relevance) and to their underlying structure (by delivering perceptual tasks that require segregated or integrated percepts). ERP results based on the mismatch negativity (MMN) show no evidence for a modulation of stream integration by attention, while stream segregation results were less clear due to overlapping attention-related components in the MMN latency range. We suggest future studies combining the proposed two-way approach with some improvements in the ERP measurement of sequential stream segregation.