For British local government elections, it is necessary to divide the total voting population into sub-groups (wards) such that each sub-group elects one or more representatives. At present there are remarkably few legal requirements governing the way in which this division is done. This study emphasizes the difficulties of formulating the problem of division, puts forward criteria which (hopefully) would look respectable and acceptable if embodied in legislation, and develops a linear programming-plus-heuristics approach which is applied to Bristol County Borough data to enable comparisons with current ward boundaries.