The cross-section of a crenellated magnet face looks like a battlement with a set of crenels and merlons. This construction provides a means for achieving uniform fields in the range 0.15 to 3 T. As the field increases and the merlon saturate, the "effective" flat face moves from the ends of the merlons to the bottom of the crenels. Thus, if z-crenellation is properly designed, the desired face shapes in the xy-plane are obtained at all field values. For triple crenellation and 1020 steel, if, for some x, y1, y2, y3 are the de positions in mils of equivalent faces for 0.15, 1.8, and 3 T, and d2 = y2 - y1, d3 = y3 - y1, the following bounds 6.2 d3 - 10 d2 ⩽2.12, 10.1 d3 - 11.2 d2 ⩾ 9.63. We discuss the origin, nature and practical use of these bounds, and we pro obtained by this method.