We investigated the operation of an all-optical rubidium-87 atomic magnetometer with amplitude-modulated light. To study the suppression of spin-exchange relaxation, three schemes of pumping were implemented with room-temperature and heated paraffin coated vacuum cells. Efficient pumping and accumulation of atoms in the F=2 ground state were obtained. However, the sought-for narrowing of the resonance lines has not been achieved. A theoretical analysis of the polarization degree is presented to illustrate the absence of light narrowing due to radiation trapping at high temperature.