In this article we report a simplified formulation of OM-pBAEs with low transfection promiscuity and capability to cross biological barriers. We have shown that a single heteromeric oligopeptide bearing arginine and histidine amino acid residues for the end modification of pBAEs is as efficient as the traditional mixture of two polymers with R and H homomeric chains, providing a simplified formulation. We have also demonstrated that conjugation of a zwitterionic peptide to the simplified formulation (pBAE-CRHR-Zw) reduces transfection by 50-fold, resulting in a less promiscuous gene delivery system. The transfection capacity of the polymer can be modulated with light by introducing a nitrobenzyl moiety. Finally, we showed that conjugation of BrainBike-4, our recently developed anti-TfR1 peptidomimetic, to pBAE-CRHR-Zw enables efficient transfection of cells with high levels of TfR1 and mediates transport across a tight monolayer of brain endothelial cells mimicking the BBB.