 New Wave reductionists typically allow for a great variety of relations backing up the analogical relation established between TR and TR*. In New Wave reduction, bridge-laws are replaced by ordered pairs of elements of the descriptive parts of the vocabularies of the two theories, which enable us to judge the degree of similarity between the derived image (which is formulated in the language of the reducing theory) and the reduced theory (Bickle 1992: 223). Reduction is associated with a space of theory-relations ranging from “perfectly smooth” or “retentive” reductions to “bumpy” reductions, which are best understood as mere replacements (Bickle 1992: 223; Hooker 1981: 45). Bickle describes smooth reductions as follows: (‘IN’ designates the derived image and ‘TO’ designates the reduced or the “old” theory):