Dexamethasone or Dexamethasone in Combination With Thalidomide as Salvage Therapy

Inclusion Criteria: * All patients must have a confirmed diagnosis of previously treated, active multiple myeloma, with hypoproliferative/low risk relapse following at least one autologous transplant. * 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 must have adequate renal function, as defined by serum creatinine \< or = 3.0 mg/dl. * Patients must be off chemotherapy (including steroids) and local radiotherapy for \> or equal 3 weeks prior to entering the study. Exclusion Criteria: * No other concurrent therapy for myeloma is permitted while on protocol. * There must be no evidence of active infection requiring IV antibiotics.