Recent years have seen major breakthroughs in genome-engineering systems, such as transposon-mediated gene delivery systems and CRISPR-Cas9-mediated genome-editing tools. In these systems, transient expression of auxiliary genes is responsible for permanent genomic modification. For both systems, it would be valuable to select for cells that are likely to undergo stable genome modification. Importantly, in particular for clinical applications of genome-engineered cell products, it will also be of importance to remove those cells that, due to random vector integration, display an unwanted stable expression of the auxiliary gene. Here, we develop a traceless selection system that on the one hand allows efficient enrichment of modified cells, and on the other hand can be used to select against cells that retain expression of the auxiliary gene. The value of this system to produce highly enriched-auxiliary gene-free cell products is demonstrated.