The phylogenetic relationships of the winged insect lineages – mayflies (Ephemeroptera), damselflies and dragonflies (Odonata), and all other winged insects (Neoptera) – are still controversial with three hypotheses supported by different datasets: Palaeoptera, Metapterygota and Chiastomyaria. Here, we reanalyze available phylogenomic data with a focus on detecting confounding and alternative signal. In this context, we provide a framework to quantitatively evaluate and assess incongruent molecular phylogenetic signal inherent in phylogenomic datasets. Despite overall support for the Palaeoptera hypothesis, we also found considerable signal for Chiastomyaria, which is not easily detectable by standardized tree inference approaches. Analyses of the accumulation of signal across gene partitions showed that signal accumulates gradually. However, even in case signal only slightly supported one over the other hypothesis, topologies inferred from large datasets switch from statistically strongly supported Palaeoptera to strongly supported Chiastomyaria. From a morphological point of view, Palaeoptera currently appears to be the best-supported hypothesis; however, recent analyses were restricted to head characters. Phylogenetic approaches covering all organ systems including analyses of potential functional or developmental convergence are still pending so that the Palaeoptera problem has to be considered an open question in insect systematics.