Precise control of gene expression is critical for biological research and biotechnology. However, transient plasmid transfections in mammalian cells produce a wide distribution of copy numbers per cell, and consequently, high expression heterogeneity. Here, we report plasmid-based synthetic circuits – Equalizers – that buffer copy-number variation at the single-cell level. Equalizers couple a transcriptional negative feedback loop with post-transcriptional incoherent feedforward control. Computational modeling suggests that the combination of these two topologies enables Equalizers to operate over a wide range of plasmid copy numbers. We demonstrate experimentally that Equalizers outperform other gene dosage compensation topologies and produce as low cell-to-cell variation as chromosomally integrated genes. We also show that episome-encoded Equalizers enable the rapid generation of extrachromosomal cell lines with stable and uniform expression. Overall, Equalizers are simple and versatile devices for homogeneous gene expression and can facilitate the engineering of synthetic circuits that function reliably in every cell.