Abatacept in Treating Adults With Mild Relapsing Wegener's Granulomatosis

Inclusion Criteria: * Diagnosis of WG, meeting at least 2 of the 5 modified American College of Rheumatology (ACR) criteria. More information about this criterion can be found in the protocol. * Relapse of WG within the past 28 days where disease activity is confined to one or more of the following sites and where the symptoms/signs are of such a nature that the usual treatment would consist of the reinstitution or increase in GC to no more than prednisone 30mg daily and/or an increase or addition of a second immunosuppressive agent other than CYC (more specific information about this criterion can be found in the protocol): 1. Sinonasal disease 2. Oral mucosa ulceration 3. Skin disease 4. Musculoskeletal disease 5. Pulmonary parenchymal disease 6. Mild ocular disease 7. Subglottic inflammation without significant stenosis 8. Otic disease 9. Breast involvement 10. Urogenital involvement 11. Other mild disease * Age of 15 years or older * Willing and able to undergo treatment and attend follow-up visits * Willing to use effective forms of contraception throughout the study Exclusion Criteria: * Disease involvement that does not meet the criteria for mild disease. More information about this criterion can be found in the protocol. * Disease activity that would usually be treated first with cyclophosphamide * Presence of disease activity for which the investigator would normally treat the participant with more than prednisone 30 mg daily. * Receiving cyclophosphamide at study entry * Treatment with prednisone at a dose of more than 15 mg daily at the time of relapse. Subjects will be eligible if prednisone was initiated or dose increased in the period between relapse and study enrollment provided that the prednisone dose was 15 mg daily or less at the time when the relapse occurred, the prednisone dosage was increased no higher than 30 mg daily following the recognition of relapse, and that the dosage increase was made no more than 28 days prior to enrollment. * Active infection * HIV infected, hepatitis C virus infected, or positive for hepatitis B * Unable to follow through with study participation * Cytopenia, defined as platelet count less than 80,000/mm3, absolute neutrophil count less than 1500/mm3, OR hematocrit less than 20% * Kidney insufficiency * Use of illegal drugs * Any other uncontrolled disease that would prevent participation * History of cancer. More information about this criterion can be found in the protocol. * Received an investigational medication or procedure within 30 days of study entry * Received a live vaccine within 4 weeks of study entry * Positive tuberculin skin test. More information about this criterion can be found in the protocol. * Tuberculosis as indicated by radiographic evidence * Past treatment with rituximab within the past 12 months, or past treatment with rituximab more than 12 months ago where the B lymphocyte count has not returned to normal * Certain other diseases. More information about this criterion can be found in the protocol. * Pregnant or breastfeeding