The paper reports regularities in the influence of the amount of waste from iron ore enrichment at a rational composition of grain components on strength of concretes with a minimal cement consumption. Low-strength concretes are used in the non-reinforced structures, so they are not subject to the requirement for the minimal cement consumption in order to ensure the protection of reinforcement against corrosion. A significant reduction in cement consumption by low-strength concretes while maintaining the required strength can be ensured by a rational grain composition of the components of a concrete mixture, which is characterized by the ratio between large, medium, and small components of 52:23:25. In such formulations, the required amount of fine-grained component is achieved by introducing the fine-grained components, made, for example, from the secondary products of industry, specifically the iron ore dressing waste. The result of the research conducted established that ensuring the rational grain composition of the concrete mixture components provides for the required low strength of concrete at a significantly less cement consumption than that for concretes whose composition is defined in line with other procedures. It was found that it is advisable to use the iron ore dressing waste as a fine-grained supplement, the introduction of which at rational amount ensures significant improvement in the efficiency of cement utilization in concretes of low strength. Application of concretes of the proposed formulations, which could be used for temporary structures ‒ a concrete cap for making floor slabs at formwork-free molding, could save a significant amount of cement, and dispose of the secondary products from industry. The research has also established that the use of plasticizers makes it possible to obtain concretes of the rational grain composition with the required workability