The present invention relates to immunomodulatory compounds, in particular a class known as IMiD TM , more specifically the compounds 4-(amino)-2-(2,6-dioxo(3-piperidinyl))-isoindoline-1,3-dione and 3-(4- Use of amino-1-oxo-1,3-dihydroisoindol-2-yl)-piperidine-2,6-dione for use in CD34 + The expression of genes for fetal hemoglobin, genes essential for erythropoiesis, and genes encoding alpha hemoglobin stabilizing proteins is induced in the cell population. These compounds are useful in the treatment of hemoglobinopathy, such as sickle cell anemia or beta-thalassemia, or anemia caused by disease, surgery, accident, or the introduction or ingestion of toxins, poisons or drugs.