We describe an approach to cancer therapy based on exploitation of common losses of genetic material in tumor cells (loss of heterozygosity) (Basilion et al., 1999; Beroukhim et al., 2010). This therapeutic concept addresses the fundamental problem of discrimination between tumor and normal cells and can be applied in principle to the large majority of tumors. It utilizes modular activator/blocker elements that integrate signals related to the presence and absence of ligands displayed on the cell surface (Fedorov et al., 2013). We show that the targeting system works robustly in vitro and in a mouse cancer model where absence of the HLA-A*02 allele releases a brake on engineered T cells activated by the CD19 surface antigen. This therapeutic approach potentially opens a route toward a large, new source of cancer targets.