Most optically pumped magnetometers based on alkali atom vapor cells and pumped by a single narrow-band laser suffer from a loss of signal since atoms become trapped in the ground state hyperfine states that are not coupled to the laser beam. This can be counteracted by additional optical repumping these ground state levels. We study hyperfine repumping using cesium vapor cells with partly overlapped ground state splitting due to their nitrogen buffer gas filling. We implement two ways of repumping and compare them to the conventional case of F=4 pumping: F=3 repumping with an additional repumper laser and combined pumping/repumping in the light-narrowing mode, where a single high-power laser is tuned near to the F=3 transitions. The three modes each are investigated for two different ways of spin-phase synchronization; the Mx and intensity modulation method. For both methods, any kind of repumping results in a clear improvement of the magnetometer sensitivity compared to operation without it, but in the Mx mode it is more pronounced (about 50 vs. 200 fT/√Hz for a 50 mm3 Cs vapor cell). The mechanisms responsible for the distinct results in the different working modes are discussed.