 This phase III trial studies tretinoin and arsenic trioxide in treating patients with newly diagnosed acute promyelocytic leukemia. Standard treatment for acute promyelocytic leukemia involves high doses of a common class of chemotherapy drugs called anthracyclines, which are known to cause long-term side effects, especially to the heart. Tretinoin may stop the growth of cancer cells by blocking some of the enzymes needed for cell growth. Arsenic trioxide may stop the growth of cancer cells by either killing the cells, by stopping them from dividing, or by stopping them from spreading. Completely removing or reducing the amount of anthracycline chemotherapy and giving tretinoin together with arsenic trioxide may be an effective treatment for acute promyelocytic leukemia and may reduce some of the long-term side effects. 