To trigger transcription termination, the ring-shaped RNA-DNA helicase Rho from Escherichia coli chases the RNA polymerase along the nascent transcript, starting from a single-stranded C-rich Rut (Rho utilization) loading site. In some instances, a small hairpin structure divides harmlessly the C-rich loading region into two smaller Rut subsites, best exemplified by the tR1 terminator from phage lambda. Here, we show that the Rho helicase can also elude a RNA structural block located far downstream from the single-stranded C-rich region but upstream from a reporter RNA-DNA hybrid. In this process, Rho hexamers do not melt the intervening RNA motif but require single-stranded RNA segments on both of its sides. The reaction is also favored by physiological glutamate ions and can implicate Rho primary recognition of 5'-YC dimers (as for Rut binding) significantly upstream (>70 nucleotides) from the intervening motif. Surprisingly, we also found that primary interactions of Rho with 2'-hydroxyl groups located upstream from the intervening RNA structure serve to elude the motif. This demonstrates that the preference of Rho for RNA residues is not limited to the secondary interaction site that mediates ATPase-fuelled mechanochemistry within the hexamer central channel. These features could be part of an energy-effective mechanism in which Brownian exploration of the conformation of the Rho-substrate complex and accommodation of downstream secondary structures within a composite primary interaction site replace ATP-dependent translocation of the Rho enzyme along corresponding structured portions of the RNA chain.