We present a large-scale density functional theory (DFT) investigation of the ABO 3 chemical space in the perovskite crystal structure, with the aim of identifying those that are relevant for forming piezoelectric materials. Screening criteria on the DFT results are used to select 49 compositions, which can be seen as the fundamental building blocks from which to create alloys with potentially good piezoelectric performance. This screening finds all the alloy end points used in three well-known high-performance piezoelectrics. The energy differences between different structural distortions, deformation, coupling between the displacement of the A and B sites, spontaneous polarization, Born effective charges, and stability is analyzed in each composition. We discuss the features that cause the high piezoelectric performance of the well-known piezoelectric lead zirconate titanate (PZT), and investigate to what extent these features occur in other compositions. We demonstrate how our results can be useful in the design of isovalent alloys with high piezoelectric performance.