The paper focuses on the problem raised in its title and verified it as a scientific hypothesis. Based on the analysis of regularities in the investigation of corruption crimes and scientific developments on the same subject, statistical data and standings of leading forensic scientists, it is proved that there are two problems: practical and scientific. The first is the presence of a negative pattern in the activities of law enforcement agencies, a kind of informal priority in the fight against minor crimes that do not represent legal and criminalistic complexity. The second problem related to the first, but already a scientific problem, is that a lot of scientific forensic developments, for example investigation techniques, are devoted to the description and investigation of just small, uncomplicated crimes. The author analyzes the causes of these problems, including methodological ones. Thus, in criminology, research programs for studying and generalizing the practice of investigating criminal cases have not been fully developed. Criminal cases that have resulted in convictions are not a completely valid and not the most informative source for a criminologist—developer. The author suggests supplementing these sources with a list of five types of, relatively speaking, «unrealized» materials.As a result, conclusions are drawn that criminology as a science should: 1) be critical of the noted practical regularity; 2) adopt the principle of priority for the development of recommendations for the investigation of the most complex and dangerous crimes. In addition, forensic techniques in cases of corruption crimes should contain a number of main areas of investigation, the essence of which is the priority of combating high—level, serial attacks, the activities of organized criminal groups and money laundering.