This paper is aimed at presenting the authors' experience to search for better performance of teaching students of economic university (school) in English. The reasons to teach Russian (or other nonanglophone) non-philological but economic students in English and its global nature are highlighted. Successful combinations of pedagogical methods and approaches are categorized as "low-tech innovations" presented in such creative industries as arts and education that are often missed by academics as well as "grand public" due to so-called "high-tech myopia". The pedosynergy effect is formally defined and its availability is logically justified. Innovative combinations of pedagogical methods and approaches as well as preparing and using joint teaching materials created in cooperation between English and professional (Marketing, Management, etc.) departments are shown as the sources creating the said pedosynergy effect. A modified model of international marketing communications including the concept of "filter of the mind" is proposed to design the test procedure permitting to assess separately contributions in an integral student performance made by English and professional departments, respectively. This procedure is considered as a tool for measuring the pedosynergy effect expected. Case studies on international business are presented as the best source to create teaching materials for socalled "in-parallel" teaching in English. Finally, the state of the Art and perspectives for further researches are drafted.