We demonstrate that the Hanle effect can be tuned between magnetically induced absorption (MIA) and magnetically induced transmission (MIT) simply by changing the polarization of the input laser beam. The experiments are done using closed hyperfine transitions of the D 2 line of 133 Cs -F g = 3 → F e = 2 and F g = 4 → F e = 5. The former shows a transformation from MIT to MIA, while the latter shows the opposite behavior. A qualitative explanation based on optical pumping and coherences among the magnetic sublevels of the ground state is borne out by a detailed density-matrix calculation. To increase the coherence time, the experiments are done in a Cs vapor cell with paraffin coating on the walls. The observed linewidth is extremely narrow (∼ 0.1 mG) compared to previous work in this area, making this a promising technique for all kinds of precision measurements.