Aminoglycosides are antibiotic drugs that act through binding to rRNA. In the search for antimicrobial amphiphilic aminoglycosides targeting bacterial membranes, we report here on the discovery of three dialkyl derivatives of the small aminoglycoside neamine active against susceptible and resistant Gram-positive and Gram-negative bacteria. One of these derivatives (R = 2-naphthylpropyl), which has good activity against MRSA and VRSA, showed a low toxicity in eukaryotic cells at 10 μM. The synthesis of amphiphilic paromamine and neamine homologous derivatives pointed out the role of the 6'-amine function of the neamine core in the antibacterial effects. The optimal number of lipophilic substituents to be attached to the neamine core and the corresponding required lipophilicity determined here should permit a more selective targeting of bacterial membranes relative to eukaryotic membranes. This work revealed the existence of windows of lipophilicity necessary for obtaining strong antibacterial effects that should be of interest in the field of antibacterial amphiphilic aminoglycosides.