The repeated execution of reasoning tasks is desirable in many applicative scenarios, such as stream reasoning and event processing. When using answer set programming in such contexts, one can avoid the iterative generation of ground programs thus achieving a significant payoff in terms of computing time. However, this may require some additional amount of memory and/or the manual addition of operational directives in the declarative knowledge base at hand. We introduce a new strategy for generating series of monotonically growing propositional programs. The proposed overgrounded programs with tailoring (OPTs) can be updated and reused in combination with consecutive inputs. With respect to earlier approaches, our tailored simplification technique reduces the size of instantiated programs. A maintained OPT slowly grows in size from an iteration to another while the update cost decreases, especially in later iterations. In this paper we formally introduce tailored embeddings, a family of equivalence-preserving ground programs which are at the theoretical basis of OPTs and we describe their properties. We then illustrate an OPT update algorithm and report about our implementation and its performance.