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Hybrid lead halide perovskites exhibit carrier properties that resemble those of pristine nonpolar semiconductors despite static and dynamic disorder, but how carriers are protected from efficient scattering with charged defects and optical phonons is unknown. Here, we reveal the carrier protection mechanism by comparing three single-crystal lead bromide perovskites: CH3NH3PbBr3, CH(NH2)2PbBr3, and CsPbBr3. We observed hot fluorescence emission from energetic carriers with ~102-picosecond lifetimes in CH3NH3PbBr3 or CH(NH2)2PbBr3, but not in CsPbBr3. The hot fluorescence is correlated with liquid-like molecular reorientational motions, suggesting that dynamic screening protects energetic carriers via solvation or large polaron formation on time scales competitive with that of ultrafast cooling. Similar protections likely exist for band-edge carriers. The long-lived energetic carriers may enable hot-carrier solar cells with efficiencies exceeding the Shockley-Queisser limit. [ABSTRACT FROM AUTHOR]