CRISPR-Cas9 genome engineering has revolutionised high-throughput functional genomic screens. However, recent work has raised concerns regarding the performance of CRISPR-Cas9 screens using TP53 wild-type human cells due to a p53-mediated DNA damage response (DDR) limiting the efficiency of generating viable edited cells. To directly assess the impact of cellular p53 status on CRISPR-Cas9 screen performance, we carried out parallel CRISPR-Cas9 screens in wild-type and TP53 knockout human retinal pigment epithelial cells using a focused dual guide RNA library targeting 852 DDR-associated genes. Our work demonstrates that although functional p53 status negatively affects identification of significantly depleted genes, optimal screen design can nevertheless enable robust screen performance. Through analysis of our own and published screen data, we highlight key factors for successful screens in both wild-type and p53-deficient cells.