In 1947, a folic acid antagonist, aminoptherin, was found to induce remission of acute leukemia in children. But this achievement was only temporary. Since then, alternatives have been found for the prevention, early detection, and sometimes cure of different members of this family of diseases. However, the adaptation of cancer to therapies is one of the aspects of this disease that continues to haunt us. At the molecular level, this adaptation is closely linked to the ability of cancer cells to alter their proteome. Such changes result from a hallmark of cancer: genomic instability and mutation. Interestingly, while researchers have found countless ways to kill cancer cells, genomic instability has not yet been explored as a cancer target. The explanations are pretty obvious: a) there is no reason to believe that reducing genomic instability kills cancer cells; in fact, genomic instability can trigger cell death, and b) genomic instability can be exploited during the execution of some successful cancer therapies. However, it is becoming increasingly apparent that genomic instability of cancer cells is the main source of tumor adaptation to treatment and the cause of immune escape in immunocompetent models. In this context, my laboratory has been asking for the last 10 years whether it is possible to kill cancer cells while preventing chromosomal instability (CIN), a type of genomic instability that triggers rapid adaptation to treatment. I will present published and unpublished research showing that certain types of cancer cells, including some from breast and ovarian origin, can be killed in vitro by drugs that induce cell death but not CIN. More surprisingly, I will present evidence that genomic instability of cells does not always precede and trigger cell killing by treatments which currently in clinical trials, hence indicating that CIN can be prevented without losing the killing power of those agents.