During chemotherapy, you’ll be given potent drugs that must be toxic enough to damage or kill leukemic cells. At the same time, they take aim at normal cells and can cause side effects. Yet, not everyone experiences side effects and people react differently. Doctors commonly combine two or more chemotherapy drugs to treat Chronic lymphocytic leukemia (CLL). Each drug type works in a different way to kill the cancerous cells. Combining drug types can strengthen their effectiveness.