This study will address the efficacy of pomalidomide in the treatment of epistaxis in patients with Hereditary Hemorrhagic Telangiectasia (HHT) who require blood transfusion or iron infusion for treatment of bleeding-induced anemia and iron deficiency. HHT is an inherited disease clinically diagnosed using the Curacao criteria, which consists of 1) spontaneous and recurrent epistaxis, 2) telangiectasias at characteristic sites, 3) visceral arteriovenous malformations (AVMs) or telangiectasias, and 4) a first degree relative with HHT (inheritance is usually autosomal dominant). Patients with three criteria are considered to have definite HHT, and those with 2 criteria probable HHT, while one or no criteria make the diagnosis unlikely 1. Patients eligible for this study will have a diagnosis of definite or probable HHT.  Estimates suggest that HHT affects between 1 in 1,330 and 1 in 10,000 individuals 2. Since many physicians are not familiar with the disease, only 10% of patients with HHT may actually be diagnosed. Significant manifestations of HHT often do not appear until the third or fourth decades, sometimes later.