The invention is directed to a method of treating a cancer in an animal and a method of increasing DNA repair activity in an animal. The methods comprise administering to an animal in need thereof an effective amount of a small molecule substance that interferes with the activity of CUL4A, such as a 1,3-benzoxathiol-2-one compound, a pyridine thione compound, a 2,6-diamino-4-thiopyran-3,5-dicarbonitrile compound, or a 1,2,4-triazole-3-thiol compound.