The maximum common substructure (MCS) problem is an important, well-studied problem in cheminformatics. It is applied in several application scenarios like molecule superimposition and scaffold detection or as a similarity measure in virtual screening and clustering. In many cases, the connected MCS is preferred since it is faster to calculate and a highly fragmented MCS is not very meaningful from a chemical point of view. Nevertheless, a disconnected MCS (dMCS) can be very instructive if it consists of reasonably sized molecular parts connected by variable groups. We present a new algorithm named RIMACS, which is able to calculate the dMCS under constraints. We can control the maximum number of connected components and their minimal size using a modified local substructure mapping approach. A formal proof of correctness is provided as well as extended runtime evaluations on chemical data. The evaluation of RIMACS shows that a small number of connected components helps us to improve MCS similarity in a meaningful way while keeping the runtime requirements in a reasonable range.