Recently I suggested a new theory of reductions in physics (Scheibe 1993, 1995, 1997). Beginning this paper I want to point out two innovations of that theory. First, the concept of reduction was not obtained by the usual analytic method of explication, i.e. no attempt was made to start out from some definite, if only vaguely understood explicandum, next to put up conditions of material adequacy in order to end up with a formally precise explicatum. Instead a ">synthetic method was suggested according to which we begin with a variety of rather special kinds of reductions and obtain the more general cases by using a natural product operation by concatenation. Second, in the new approach it is not required that the reduction of a theory has to include its fundamental assumptions. Rather a concept of partial reduction was developed in which we have to satisfy ourselves by reducing only this or that consequence of the theory to a corresponding consequence of the reducing theory. Both novelties were not the result of a deliberate act but were dictated by the very situation that we encounter in physics. It seems that widely differing theory reductions, in particular approximative ones, are accepted by physicists (although they might not be aware of this) and that the uselessness of the reduction theories hitherto developed goes back to the circumstance that each of them is characterized by one single, very general concept of reduction totally inadequate to cope with the complexity of the situation. Moreover, there are notoriously recalcitrant cases of theories as, for instance, classical mechanics vis-à-vis quantum mechanics that defy all attempts of their total reduction whereas we do know of many partial reductions in the sense indicated.