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Comprehensive climate models exhibit a large spread in the magnitude of projected poleward eddy-driven jet shift in response to warming. The spread has been connected to the radiative response to warming. To understand how different radiative assumptions alone affect the jet shift in response to warming, we introduce a new clear-sky longwave radiation hierarchy that spans idealized (gray versus four bands; without or with interactive water vapor) through comprehensive (correlated-k) radiation in the same general circulation model. The new hierarchy is used in an aquaplanet configuration to explore the impact of radiation on the jet stream response to warming, independent of mean surface temperature and meridional surface temperature gradient responses. The gray radiation scheme produces a split jet and its eddy-driven jet shifts equatorward as climate warms, whereas the storm track shifts equatorward then poleward. Including four longwave bands leads to a merged jet that shifts slightly poleward with warming, and the storm track shifts monotonically poleward. Including interactive water vapor makes the poleward jet shift comparable to the jet shift with comprehensive radiation and interactive water vapor. These jet and storm track differences are linked to the radiation response of the stratospheric temperature, the tropopause height, and the meridional gradient of the radiative forcing to warming. Dynamically, the equatorward jet shift with the gray scheme is consistent with reduced wave reflection on the poleward flank of the jet, whereas the poleward jet shift with the other schemes is consistent with increased eddy length scale that favors equatorward wave propagation.