Many materials can only be recycled a limited number of times because of physical degradation (paper and board), chemical degradation (plastics), or impurities (several metals). Management of the quality of materials is a key to high long-term recycling rates and, hence, to the sustainable future. This key includes several elements, such as: retaining the quality of materials in the production and use of products; retaining the quality of materials in the recycling processes; and using high-quality materials only when it is required. Pinch analysis is a set of methods to optimize physical flows by taking the quality into account. It was originally developed for minimizing the energy demand in process industries. It has been adapted for optimization also of water and solvents flows. A Japanese research group applied part of the method on flows of steel within Japan and globally. We present a pilot study that illustrates how all the elements of the basic pinch approach can be applied to global systems of material flows. Our material pinch analysis (MPA) distinguishes between three categories of steel applications, each with its own requirements on the material quality: rolled steel, sections and re-bar. Copper in wiring etc. increases the copper content of steel recycled from machinery and eventually restricts the recyclability of the steel in a global system where steel use does not increase. This is important because an MPA is mainly relevant when impurities or other quality aspects restrict the recycling rate. Our quantitative results should not be considered accurate reflections of the reality, because the pilot study is to a large extent based on assumptions and crude data. However, the model gives a first indication that the maximum recycling rate of steel is approximately 80% in a potential future when steel use does not increase, unless technology is improved. A full MPA with more thorough data collection would more accurately define the maximum long-term recycling rate and the minimum quantity of ore-based material. In addition, a full MPA would give information on for what applications ore-based material should be used, and what scrap flows should be discarded rather than recycled. Such information can be important for policy-making aiming at increased resource efficiency. If it is important for policy-making it is also likely to be important to industrial companies that can be affected by policies.