The diversification of modern birds has been shaped by a number of radiations. Rapid diversification events make reconstructing the evolutionary relationships among taxa challenging due to the convoluted effects of incomplete lineage sorting (ILS) and introgression. Phylogenomic data sets have the potential to detect patterns of phylogenetic incongruence, and to address their causes. However, the footprints of ILS and introgression on sequence data can vary between different phylogenomic markers at different phylogenetic scales depending on factors such as their evolutionary rates or their selection pressures. We show that combining phylogenomic markers that evolve at different rates, such as paired-end double-digest restriction site-associated DNA (PE-ddRAD) and ultraconserved elements (UCEs), allows a comprehensive exploration of the causes of phylogenetic discordance associated with short internodes at different timescales. We used thousands of UCE and PE-ddRAD markers to produce the first well-resolved phylogeny of shearwaters, a group of medium-sized pelagic seabirds that are among the most phylogenetically controversial and endangered bird groups. We found that phylogenomic conflict was mainly derived from high levels of ILS due to rapid speciation events. We also documented a case of introgression, despite the high philopatry of shearwaters to their breeding sites, which typically limits gene flow. We integrated state-of-the-art concatenated and coalescent-based approaches to expand on previous comparisons of UCE and RAD-Seq data sets for phylogenetics, divergence time estimation, and inference of introgression, and we propose a strategy to optimize RAD-Seq data for phylogenetic analyses. Our results highlight the usefulness of combining phylogenomic markers evolving at different rates to understand the causes of phylogenetic discordance at different timescales.