Variants of cytotoxic T-lymphocyte antigen 4 (CTLA-4) with high affinity, potency and stability. Formulations of CTLA-4 variants at high concentration for subcutaneous or intravenous administration, e.g. at monthly or less frequent dosage intervals. Use of CTLA-4 variants for treating rheumatoid arthritis and other inflammatory disorders. Fusion of CTLA-4 with IgG Fc having improved stability and longer in vivo half-life.