The behavior of Self-Compacting Concrete (SCC) is very sensitive to the use of by-products in replacement of conventional cement or finer aggregate fractions. The high proportions of these raw materials in SCC can in great part explain this performance. 18 SCC mixes of slump-flow class SF3 were prepared for a thorough evaluation of different sustainable materials and for the prediction of their effects as binder or fine/powder aggregate on the mechanical properties of SCC. The mixes incorporated 100% coarse Recycled Concrete Aggregate (RCA); different amounts (0%, 50% or 100%) of fine RCA; CEM I ordinary Portland cement and CEM III/A (with 45% ground granulated blast furnace slag); and more sustainable powders compared to conventional limestone filler <0.063 mm (such as limestone powder 0/0.5 mm and RCA powder 0/0.5 mm). Flowability, hardened density, strength under compression, tensile and bending stresses and modulus of elasticity were all studied. The addition of 50% fine RCA yielded an SCC of adequate strength, stiffness and flowability. SCC manufactured with limestone powder 0/0.5 mm showed the best overall performance, while SCC behavior was improved when adding CEM III/A by adjusting the mix composition. The experimental results of all the mechanical properties were compared with the values predicted by the compressive-strength-based formulas from the European and USA standards. Overall, the values resulting from those expressions overestimated all the mechanical properties. Therefore, since all these properties followed the same simple-regression trend, a statistical analysis was performed to develop a global model capable of accurately predicting them all.