The lack of a demarcation between international criminal law ( icl ) and public international law ( pil ) creates a set of complex issues resulting from their overlap. A prime example of this situation is the tension between the state duties under icl , to investigate and prosecute ius cogens crimes, even if they are committed by the highest representatives of foreign states, and the pil customary rules on the latter’s personal and functional immunity from foreign criminal jurisdiction. Attempts by the icj and the ilc Special Rapporteur to limit this tension have been met with strong criticism. The various arguments against both approaches show the significant difficulties to overcome the tensions caused by the overlap between icl and pil . In light of this situation, a stricto sensu definition of icl should be adopted as a way to establish a clearer demarcation between icl and pil and to limit the scope of their overlap.