According to observations, a large relative humidity with respect to ice, RHi >> 100%, often persists outside and inside upper tropospheric cirrus ice clouds. The persistence of the large in-cloud RHi means that H2O is slowly deposited onto cloud ice crystals. This unusual physical situation is similar to one in which a released body would slowly fall owing to gravitation. Here we present a physical mechanism which can be responsible for the persistence of large in-cloud RHi. We find that clear-sky RHi up to 176% can be built up prior to the formation of ice cirrus by the homogeneous freezing of aqueous droplets containing H2SO4 and HNO3. As the droplets are cooled, a phase separation, which Occurs during freezing, leads to the formation of a residual solution coating around the ice crystals formed. The coating can serve as a shield, slowing the rate of ice growth by similar to 10(3) in comparison with uncoated ice, and this can be a reason for the persistence of the large in-cloud RHi.