The work proposes a thermodynamic method for increasing the effectiveness of the polytropic and adiabatic compression processes. The method is further used for improving the COP of the compression refrigeration cycles. The method theory is considered. A theorem proved here shows that ideal method application leads to the isothermal compression operation. The method application is illustrated by schemes running with single, two-stage and multi-stage compression, for the air conditioning, normal and industrial refrigeration. According to the proposal, the compression refrigeration should stimulate the compressor operation with high temperature discharge gas and the conversion of its heat into work, rather than using an additional compression work for limiting the discharge gas temperature, as it is happening today in the two-and multi-stage refrigeration. The schemes' operation has been modelled. The model results emphasize a reasonable feasibility of the single-stage, but the three-stage and especially the two-stage compression are the most feasible, enjoying a great potential in the refrigeration COP increase, and therefore in the primary energy savings and carbon footprint reduction (similar to 50-100% and more). (C) 2011 Elsevier Ltd. All rights reserved.