The most potent compounds, including 19f, which blocks HDAC1, HDAC2, and HDAC3, as well as the selective HDAC1/HDAC2 inhibitors 21a and 29b, were selected for further cellular testing against human acute myeloid leukemia (AML) and erythroleukemic cancer (HEL) cells, taking into consideration their low toxicity against human embryonic HEK293 cells. This evidence concerns the gene HDAC2 and acute myeloid leukemia.