Inclusion Criteria:

• All patients must have a confirmed diagnosis of previously treated, active multiple myeloma, with relapse or progression following at least one autologous transplant. High risk is defined as any one of the following at the time of relapse:a) Plasma cell labeling index (PCLI) > 1%, b) Bone marrow plasmacytosis > or = 30%, c)Bartl grade >or = 2 on bone marrow biopsy, or d)Cytogenetic abnormalities of chromosome 13, 11q, or any translocation at the time of relapse.
• Patients must be 18 years of age or older. Women of childbearing age and fertile men must use a medically acceptable means of birth control while on study and for 6 months thereafter.
• Patients must sign an informed consent to participate in this study, and be fully aware of the known teratogenic potential of this drug combination.
• Patients must have a SWOG performance status of 0-2. Patients with a poor performance status (3-4) based solely on bone pain, will be eligible.
• Patients must have adequate renal function, as defined by serum creatinine < or = 3.0 mg/dl
• Before starting treatment, women of childbearing potential should have a negative pregnancy test performed within 24 hours prior to beginning therapy. Written report of a negative pregnancy test must be obtained before a prescription for thalidomide is issued. Pregnancy testing is not required for 1) women wh have been post-menopausal for at least 2 years with no menses, 2) women who have had a hysterectomy.
• Patients must have adequate bone marrow function, as defined by platelet count of 150,000/microliter, unless explained by extensive marrow plasmacytosis.
• Patients must be off chemotherapy (excluding steroids) and local radiotherapy for > 3 weeks prior to entering the study

Exclusion Criteria:

• There must be no evidence of active infection requiring IV antibiotics
• No other concurrent therapy for myeloma is permitted while on protocol