Human immunodeficiency virus (HIV) reverse transcriptase (RT)-associated ribonuclease H (RNase H) remains as the only enzyme encoded within the viral genome not clinically validated as an antiviral target. We have previously reported that the galloyl derivative II-25 had RNase H inhibitory activity in enzymatic assays but showed weak antiviral activity in phenotypic assays due its large polarity and poor membrane permeability. In this report, we report on a series of II-25 derivatives, obtained by addition of different hydrophobic moieties ("the wings") at the C-2 and C-3 positions of the piperazine ring that showed improved RNase H inhibitory activity. Six compounds showed strong inhibitory activity and were found to be more potent than β-thujaplicinol in enzymatic assays. The most potent compound was IA-6 and exhibited the best inhibitory activity (IC<sub>50</sub> = 0.067 ± 0.02 μM). IA-6 was around 11 and 30 times more potent than II-25 and β-thujaplicinol, respectively. Molecular modeling studies predict a strong hydrophobic interaction between the furylmethylaminyl group of IA-6 and the side chain of His539, explaining the potent HIV-1 RNase H inhibition. Unfortunately, none of the derivatives showed significant antiviral activity in cell culture. It is worth emphasizing that most of the obtained compounds show low cytotoxicity (CC<sub>50</sub> > 20 μM), which confirms the significance of identifying galloyl derivatives as valuable leads for further optimization.