The exclusive dimension d = D(f) of a Boolean function f with respect to some input order is a lower bound on the size of all complete decision diagrams for f, and most ordered decision diagrams from the (vast) literature are shown to be complete. Any complete diagram for f can be efficiently reduced to a multi-linear diagram of minimal size d, and all minimal diagrams are linearly similar. The Least Ordered Diagram LOD(f) of function f is the unique ordered diagram whose base has the least possible values. Efficient bit and word level algorithms are shown to perform logical operations on least diagrams. The theoretical comparison favors LOD over BDD: the larger the computer word size, the better. In the average and worst cases, the size of LOD(f) is near the square root of the size of BDD(f)..