Ionic transport in charged conical nanopores is known to give rise to ion current rectification. The present study shows that the rectification direction can be inverted when using electrolyte solutions at very low ionic strengths. To elucidate these phenomena, electroneutral conical nanopores containing a perm-selective region at the tip have been investigated and shown to behave like classical charged nanopores. An analytical model is proposed to account for these rectification processes.