One option to improve the cycle efficiency of current state-of-the-art aero engines is to increase the turbine inlet temperature. Since this temperature is above the melting temperature for the alloys utilised in the turbine component already today, efficient cooling methods must be developed that consider both aerodynamic and aerothermal aspects of cooling. Here, the goal is to extract as little as possible secondary air from the main hot gas cycle for cooling and to use this coolant then aerodynamically and aerothermally as efficient as possible. The paper to be presented documents a CFD based design approach that lead to a new passive shroud cooling concept and the definition of its operational parameters. By using a simple one dimensional method [10] for predicting the aerodynamic losses resulting from such a cooling configuration in connection with 3d Navier-Stokes solvers (RANS) for predicting film cooling effectiveness contours on the rotor shroud surfaces, the new cooling configuration was developed. The concept was then tested and confirmed experimentally as documented in more detail in Part 2 of this paper. It is noted that only 70% of the coolant mass flow required for the current configuration was used for the new concept whereas the aerodynamic efficiency measured remained nearly constant. Improving upon existing passive shroud cooling systems where the coolant is injected directly into the labyrinth of the shroud, the new approach comprises cooling holes that inject the coolant upstream of the labyrinth and through the stator platform into the main passage flow. Here, it is important that the bulk of the coolant is placed below the dividing streamlines between main passage flow and labyrinth flow. Thereby, it can be achieved that the major part of the coolant indeed reaches the thermally loaded target surfaces on the shroud bottom at various axial gaps due to different operating points of the turbine. Besides the improved film-cooling effectiveness measured, the second important aspect of the new concept is the achievement of as small as possible additional aerodynamic losses due to coolant ejection into a high speed flow region. It will be shown that both goals can be achieved by the new concept. Furthermore, CFD results on film-cooling performance and aerodynamic losses will be shown and compared with experimental data.