A previous finite-size study for the chiral phase transition of two-flavor QCD is extended to a smaller quark mass of mq=0.0125 in lattice units. The characteristics of the system for lattice sizes (63 - 123) × 4 are found to be quite similar to those for mq=0.0025. The increase of susceptibilities over this range of the spatial size is still too mild to discriminate among the order of the transition also at this small quark mass.