 This is a single-arm, open-label study that will investigate the efficacy and safety profile of pomalidomide in patients with genetically-documented Hereditary Hemorrhagic Telangiectasia defined by characteristic mutations in Eng, Alk-1 or Smad-4 or idiopathic vascular ectasia with no documented mutations, leading to refractory bleeding of the small bowel. This study will be limited to patients with documented bleeding from the small bowel, including the duodenum, jejunum or ileum. Eligible patients will be dependent on transfusion or intravenous iron therapy requiring at least 4 units of blood transfusion or 4 iron infusions over the preceding 4 months and will have endoscopically-confirmed areas of vascular ecstasia. Therapy for all eligible patients will be initiated with a 1 mg daily dose of pomalidomide. The principal investigator will determine whether intrapatient dose escalation is indicated based on the response of the patients bleeding during the first 30 days of therapy. If dose escalation is indicated, pomalidomide will be increased at the investigators discretion to a maximal dose of 5 mgday. Cessation of GI bleeding will be defined as maintenance of stable hemoglobin without blood transfusion or intravenous iron therapy over a 4 week period. Once GI bleeding has ceased, patients will be maintained at a stable pomalidomide dose for an additional 4 months, and the dose then tapered by 1 mg per month, or until bleeding recurs. Patients will be followed for a total of six months post-therapy to determine whether the response is maintained. 