RecG differs from most helicases acting on branched DNA in that it is thought to catalyze unwinding via translocation of a monomer on dsDNA, with a wedge domain facilitating strand separation. Conserved phenylalanines in the wedge are shown to be critical for DNA binding. When detached from the helicase domains, the wedge bound a Holliday junction with high affinity but failed to bind a replication fork structure. Further stabilizing contacts are identified in full-length RecG, which may explain fork binding. Detached from the wedge, the helicase region unwound junctions but had extremely low substrate affinity, arguing against the "classical inchworm" mode of translocation. We propose that the processivity of RecG on branched DNA substrates is dependent on the ability of the wedge to establish strong binding at the branch point. This keeps the helicase motor in contact with the substrate, enabling it to drive dsDNA translocation with high efficiency.