Neutron-deficient astatine and francium nuclei were produced in the reaction 30Si+181Ta→211Fr* at 152 MeV. The evaporation residues from this very fissile system were selected with the HERCULES-II detector system and residue-gated γ rays were measured with Gammasphere. Excited states were observed for the first time in Fr205,207, as well as sequences of low-energy transitions between high-spin states in At204 and Fr206. These latter structures have properties similar to those associated with magnetic rotation (shears bands) in lead nuclei. Comparisons with established shears bands are presented and prospects for the magnetic-rotation phenomenon near the predicted N=120 "magic" number are explored.