Factorial designs of resolution III are such that all main effects are estimable, ignoring two-factor interactions and all higher order interactions. Designs of resolution IV are such that all main effects are estimable with no two-factor interactions as aliases, ignoring all higher order interactions. The general technique for producing 2ndesigns of resolution IV is a specific application of the Box-Wilson “fold-over” theorem. Recent work by Steve Webb on resolution IV designs for two-level factors is discussed and extended. The miniium run requirement for a 2nresolution IV design is 2n. It is proved that if a minimal resolution IV 2ndesign has each factor occurring equally often at its high and low levels, then the design must be a fold-over design. A proof that the minimum run requirement for a resolution IV 2n3mdesign,m> 0, is 3(n+ 2m− 1) also is included. Minimal 2nresolution IV designs are presented for various values ofn. All these designs can be run innblocks of size 2 each.