3(2n–2) designs may bedivided into two blocks, one of size 2n–1and the other of size 2n–2by blocking on one of the defining contrasts and into three blocks of size 2n–2by blocking on all three defining contrasts. Blocking on an effect which is not a defining contrast gives two blocks of 3(2n–3) runs each. In this paper these methods are applied to 3(2n–k) designs with twelve or twenty-four points. The designs considered are the 3(24–2) and 3(25–2) designs with all main effects and all two factor interactions estimable (assuming that higher order interactions are negligible), and saturated main effect plans with twelve points and up to eleven factors.