The court with authority for cassation is the Supreme Court. However, the Supreme Court operates in different compositions. Each of them has specific statutory competence to review cases as the cassation court. At the same time, for the sake of ensuring the uniform and consistent court practice, a new algorithm has been introduced by law for determining the composition of the cassation court by jurisdiction “assignment” all the way from the panel to the Grand Chamber. This article focuses on the analysis of separate problematic issues with regard to determining a legally competent composition of the cassation court and ensuring the right of an individual to a hearing by “a tribunal established by law” (in terms of Article 6 of the Convention for the Protection of Human Rights and Fundamental Freedoms); the purpose of this article is also to draft proposals targeted at solving the said issues. The author has identified the main practical problems arising with the application of the “hierarchy principle” in respect of the mechanism of case referral for consideration by the chamber, the joint chamber or the Grand Chamber; disagreement with some legal implications; the consequence of jurisdiction assignment; acceptance and refusal to accept a referred case and conduct respective proceedings; the concept of “opinion on the application of the provision of law in the context of similar legal relations”; abuse relating to referral of a case for consideration of the Grand Chamber; the concept of “a need to withdraw” from the opinion; disclosure of the opinion of judges on the merits before the case is resolved. The mechanism of jurisdiction assignment generally conforms to the objective of the Supreme Court to ensure the uniform and consistent court practice. At the same time, procedural law contains provisions which may get ambiguous interpretation in practice and thus may entail procedural complications. The author suggests the below ways to prevent them. If it is necessary to withdraw from two or more opinions of the panel, the chamber or the joint chamber, the case shall be referred to the Grand Chamber of the Supreme Court; A consistent mechanism of jurisdiction assignment should be introduced: panel – chamber; chamber – joint chamber, joint chamber (in fact, the superior body of a relevant court of cassation) – the Grand Chamber. The right to refer a case for the reasons of an exclusive legal problem should fall within the competence of the joint chamber. This eliminates the risk of abuse related to referral of cases, with cassation courts becoming the principal body for ensuring the consistency of practice. The Grand Chamber should not refuse to accept a case for consideration if it is referred by the joint chamber of a relevant court of cassation. To check the validity of an appeal with regard to the alleged breach of jurisdiction, and if the Grand Chamber has already filed its legal opinion, the panel should act taking this opinion into account, and if it has not – to refer it to the Grand Chamber. To determine the criteria of “withdrawal” and generally the concept of interaction between judges with the aim of ensuring the consistency of court practice.