Efficacy of CC-5013 (Revlimid or Lenalidomide) in Patients With Primary Systemic Amyloidosis

1. Histochemical diagnosis of amyloidosis as based on detection by polarizing microscopy of green birefringent material in Congo red-stained tissue specimens and immunohistochemical proof of AL 2. Measurable disease of AL amyloidosis as defined by one of the following: * Serum monoclonal protein \>=1.0 g by protein electrophoresis * \>200 mg of monoclonal protein in the urine on 24 hour electrophoresis * Serum immunoglobulin free light chain \& \>=10 mg/dL AND abnormal serum immunoglobulin kappa to lambda free light chain ratio 3. ECOG performance status (PS) 0, 1, 2, or 3 4. \>=18 years of age 5. The following laboratory values obtained \<=14 days prior to registration: * Creatinine \< = 3 mg/dL * Absolute neutrophil count \>=1000/microliter * Platelet \>=75000/microliter * Hemoglobin \> = 8.0 g/dL 6. Symptomatic organ involvement with amyloid to justify therapy. This could include liver involvement, cardiac involvement, renal involvement, peripheral neuropathy grade 1, or soft tissue involvement. Must have more than purpura or carpal tunnel syndrome 7. Previously treated or untreated. No limit to prior therapy provided there is adequate residual organ function 8. Ability to provide informed consent 9. Anticipated life expectancy of at least 3 months 10. None of the following: * Pregnant women or women of reproductive ability who are unwilling to use effective contraception * Nursing women * Men who are unwilling to use a condom (even if they have undergone a prior vasectomy) while having intercourse with any woman, while taking the drug and for 4 weeks after stopping treatment * Myelosuppressive chemotherapy \< 4 weeks prior to registration * Concomitant high dose corticosteroids * Grade 2 (or higher) peripheral neuropathy * Uncontrolled infection * Clinically overt multiple myeloma * Active malignancy * Prior hypersensitivity reaction to Thalidomide * Syncope within the past 30 days