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In unsupervised domain adaptation (UDA), directly adapting from the source to the target domain usually suffers significant discrepancies and leads to insufficient alignment. Thus, many UDA works attempt to vanish the domain gap gradually and softly via various intermediate spaces, dubbed domain bridging (DB). However, for dense prediction tasks such as domain adaptive semantic segmentation (DASS), existing solutions have mostly relied on rough style transfer and how to elegantly bridge domains is still under-explored. In this work, we resort to data mixing to establish a deliberated domain bridging (DDB) for DASS, through which the joint distributions of source and target domains are aligned and interacted with each in the intermediate space. At the heart of DDB lies a dual-path domain bridging step for generating two intermediate domains using the coarse-wise and the fine-wise data mixing techniques, alongside a cross-path knowledge distillation step for taking two complementary models trained on generated intermediate samples as 'teachers' to develop a superior 'student' in a multi-teacher distillation manner. These two optimization steps work in an alternating way and reinforce each other to give rise to DDB with strong adaptation power. Extensive experiments on adaptive segmentation tasks with different settings demonstrate that our DDB significantly outperforms state-of-the-art methods. Code is available at https://github.com/xiaoachen98/DDB.git.