In their timely Perspective article (Kazanina, N. & Tavano, A. What neural oscillations can and cannot do for syntactic structure building. Nat. Rev. Neurosci. 24, 113–128 (2023))1, Kazanina and Tavano argue that neural oscillations cannot linearly chunk (or segment) speech into syntactic constituents because constituents are defined in terms of hierarchical relations. Instead, they propose that oscillations could support syntactic structure building (SSB) through ‘multi-scale integration’ of hierarchically organized constituents. We agree with their arguments against the utility of chunking for SSB. However, the dichotomy between ‘oscillations for chunking’ and ‘oscillations for integration’ does not accurately represent the literature: the integratory role of oscillations is well-accepted2,3, and chunking is not a candidate model of SSB. Here, we show that recent work on oscillations and syntax4,5 does not assume chunking and we identify principal challenges for the integration proposal put forward by Kazanina and Tavano.