As a preliminary matter, the article considers different legal regimes pertaining to the power of the international criminal tribunals to punish conduct that tends to impede or frustrate the good administration of justice, from Nuremberg to the UN Mechanism for International Criminal Tribunals. It further examines the actus reus and mens rea of the offence of giving false testimony under solemn declaration, pursuant to article 70(1)(a) of the Rome Statute. It separately evaluates whether materiality of the false testimony is a requisite legal element of this offence. In conclusion, the article observes that few offences are carried off with greater impunity in the international criminal proceedings, and cautions against establishing false testimony as norm through a deliberate non-enforcement of its prohibition.