Migratory birds use multiple compass systems for orientation, including a magnetic, star and sun/polarized light compass. To keep these compasses in register, birds have to regularly update them with respect to a common reference. However, cue-conflict studies have revealed contradictory results on the compass hierarchy, favoring either celestial or magnetic compass cues as the primary calibration reference. Both the geomagnetic field and polarized light cues present at sunrise and sunset have been shown to play a role in compass cue integration, and evidence suggests that polarized light cues at sunrise and sunset may provide the primary calibration reference for the other compass systems. We tested whether migratory garden warblers recalibrated their compasses when they were exposed to the natural celestial cues at sunset in a shifted magnetic field, which are conditions that have been shown to be necessary for the use of a compass reference based on polarized light cues. We released the birds on the same evening under a starry sky and followed them by radio tracking. We found no evidence of compass recalibration, even though the birds had a full view of polarized light cues near the horizon at sunset during the cue-conflict exposure. Based on a meta-analysis of the available literature, we propose an extended unifying theory on compass cue hierarchy used by migratory birds to calibrate the different compasses. According to this scheme, birds recalibrate their magnetic compass by sunrise/sunset polarized light cues, provided they have access to the vertically aligned band of maximum polarization near the horizon and a view of landmarks. Once the stars appear in the sky, the birds then recalibrate the star compass with respect of the recalibrated magnetic compass. If sunrise and sunset information can be viewed from the same location, the birds average the information to get a true geographic reference. If polarized light information is not available near the horizon at sunrise or sunset, the birds temporarily transfer the previously calibrated magnetic compass information to the available celestial compasses. We conclude that the type of cue-conflict manipulation and the availability of stars can explain the discrepancies between studies.