The development of Zn2+-dependent dimethyl-dppz-PNA conjugates (PNAzymes) as efficient site-specific artificial ribonucleases enables rapid sequence-specific degradation of clinically relevant RNA target sequences, but the significance of the RNA/PNAzyme sequence and structural demands for the identification of novel RNA targets are not fully understood. In the present study, we investigated the influence of sequence variation in the recognition arms of the RNA/PNAzyme complex on the RNA cleavage activity of the artificial enzymes. The base pairs closing the 3-nucleotide bulge region on both sides of the bulge as well as the neighbouring nucleobases were shown to significantly influence the RNA cleavage activity. Elongation of the RNA/PNAzyme complex was shown to be tolerated, although potentially prohibitive for catalytic turnover. The specificity of PNAzyme action was clearly demonstrated by the significantly reduced or absent cleavage activity in complexes containing mismatches. Further investigation into 2- and 4-nucleotide RNA bulges indicated that formation of 3-nucleotide bulges in the target RNA gives the optimal cleavage rates, while some potential off-target cleavage of formed 4-nucleotide bulges of select sequences should be considered.