Bleeding is a common problem in concrete slabs, and may lead to serious damage. The goal of this article is to understand the impact of alternative binders and their properties on the bleeding of concrete. Therefore, the impact of the type of binder on the bleeding process is investigated. The results show that the addition of granite powder or fly ash allows for the increased control of the bleeding process. It was found that a finer particle size distribution (PSD), an increased specific surface area (SSA), and a higher bulk density may reduce the amount of dispensed water in the concrete mix. Furthermore, the use of additives with an increased SSA leads to even a 30% reduction of the bleeding rate of mixes. The utilization of additives with a finer PSD than cement enables a 37% reduction of the bleeding rate of mixes. The influence of bleeding on compressive strength was assessed using destructive and non-destructive tests: Replacing 30% of cement with granite powder leads to a 30% reduction of concrete strength after 28 days of curing; on the other hand, replacing 30% of cement with siliceous fly ash leads to an 18% reduction of strength. Importantly, bleeding was also found to lead to the heterogeneity of the physical and mechanical properties across the concrete section. Consequently, the proper control of the bleeding process leads to more homogeneous properties of concrete across its cross-section.