Wonderment et al -
The relevant part
of the ICC statute:
The principle of “complementarity” provides that certain cases will be inadmissible even though the Court has jurisdiction. In general, a case will be inadmissible if it has been or is being investigated or prosecuted by a State with jurisdiction. However, a case may be admissible if the investigating or prosecuting State is unwilling or unable to genuinely to carry out the investigation or prosecution. For example, a case would be admissible if national proceedings were undertaken for the purpose of shielding the person from criminal responsibility. In addition, a case will be inadmissible if it is not of sufficient gravity to justify further action by the Court.
Trials that result in light punishments would be very unlikely to trigger that "unwilling or unable" exception. So should anybody in the US be paranoid about the ICC? No. Is it going to fulfill lefty fantasies of providing judicial judgement on the Bush Administration? Also no.