The invention provides antibody heavy chain constant regions with a hinge region modified to reduce binding to Fcγ receptors. The modification occurs within positions 233-236 by replacement of natural residues by glycine(s) and/or deletion(s). Such modifications can reduce binding of an antibody bearing such a constant region to Fcγ receptors to background levels. The constant regions can be incorporated into any format of antibody or Fc fusion protein. Such antibodies or fusion proteins can be used in methods of treatment, particularly those in which the mechanisms of action of the antibody or Fc fusion protein is not primarily or at all dependent on effector functions, as is the case when an antibody inhibits a receptor-ligand interaction or agonizes a receptor.