The article discusses the main problems associated with a courts consideration of a criminal case received after a shortened inquiry. The purpose of the article is to review features of the courts study and assessment of evidence in this category of criminal cases. The author substantiates the need to preserve accelerated proceedings in Russian criminal proceedings, but insists on certain advantages of changing the regulatory model of reduced inquiry. The main attention in the article is given to contradictions in the normative regulation of the trial of criminal cases received by the court with an indictment. The article analyzes some features of substantiation in this category of criminal cases both in pre-trial and in judicial proceedings. Theoretical material is illustrated by examples from judicial practice. The author suggests changing the court proceedings on this category of criminal cases, reducing the list of grounds for returning the criminal case to the prosecutor, and expanding the rights of the accused.