Study to Determine the Maximum Tolerated Dose, Safety and Effectiveness of Pomalidomide for Patients With Sickle Cell Disease

Inclusion Criteria: * Ages 18 to 60 years, inclusive, at the time of signing the informed consent form * Clinically significant Sickle Cell Disease (SCD) documented as Sickle Cell Anemia or Sickle Beta-Zero Thalassemia * Clinically significant SCD defined as at least 1 documented pain episode per year averaged over the past 3 years or one episode of active leg ulcers, priapism, or acute chest syndrome over the past 3 years * Failed to achieve at least an absolute 5% increase in hemoglobin F while taking Hydroxyurea (HU) or unable to tolerate HU as described by the treating physician and may include but is not limited to lack of efficacy (such as people who have continued to have pain episodes more than 2 times a year or who have had acute chest or multiorgan failure syndromes or an episode of priapism), or other severe side effects while on HU (severe side effects include significant myelosuppression; skin cancer; or cytotoxicity evidenced by gastrointestinal symptoms, dermatological reactions, hepatic enzyme elevations, pulmonary fibrosis or neurological disturbances), or refusal of hydroxyurea therapy by the informed patient * Able to adhere to the study visit schedule and other protocol requirements * Females must be surgically sterile (post hysterectomy or bilateral oophorectomy) or naturally postmenopausal for at least 24 consecutive months (i.e., have not had menses at any time in the preceding 24 consecutive months) * Male subjects must agree to use a latex condom during any sexual contact with females of child bearing potential (FCBP) during study drug treatment, during dose interruptions, and for at least 28 days following discontinuation of study drug even if they have undergone a successful vasectomy. Counseling about the requirement for latex condom use during sexual contact with FCBP and the potential risks of fetal exposure must be conducted at a minimum of every 28 days. * Male subjects must agree to abstain from donating semen or sperm while taking study drug and for 28 days after stopping study drug. * Both males and females must agree to abstain from donating blood while taking study drug and for 28 days after stopping study drug. * Both males and females must agree that they will not share study drug and will be counseled about the potential risks of fetal exposure. Exclusion Criteria: * Known positive status for human immune virus (HIV), Hepatitis B; or acute/chronic, active Hepatitis C * Any serious medical condition, laboratory abnormality, or psychiatric illness that would prevent the subject from signing the informed consent form * Females of childbearing potential, pregnant or lactating females * Any condition, including the presence of laboratory abnormalities, which place the subject at unacceptable risk if he/she were to participate in the study or confounds the ability to interpret data from the study * Subjects unlikely to comply with birth control, medication dosing, or study visit requirements * Subjects with severe or life threatening, active, unresolved infections * Any of the following laboratory abnormalities derived from the Screening Visit: * Platelet count or white blood cell count (WBC) less than the lower limit of normal (LLN) * Total hemoglobin less than or equal to 6.0 g/dL * Hemoglobin A (HbA) from transfusion greater than 20% at baseline * Creatinine greater than Upper Limit of Normal (ULN) * Alanine Aminotransferase / Serum Glutamic Pyruvic Transaminase (ALT/SGPT) greater than 3 x ULN * Total bilirubin greater than 10 mg/dL * Subjects on a chronic transfusion program * History of non-catheter related Deep Vein Thrombosis (DVT) or stroke * Chronic symptomatic constipation * History of cancer (except basal cell or squamous cell carcinoma or carcinoma in situ of the cervix or breast) unless the subject has been free of disease for at least three years. * Use of agents that can induce fetal hemoglobin within 90 days (three months) of Day 1 (i.e. HU, butyrates, decitabine, 5-azacytidine, or erythropoietin) * Use of experimental drug or treatment within 30 days of the first dose of study drug * History of allergic reaction to thalidomide or lenalidomide * Prior desquamating (blistering) rash while taking thalidomide or lenalidomide * Greater than or equal to a Grade 2 neuropathy