The aim of this paper is, first, to recall fuzzy relational compositions (products) and, to introduce an idea, how the so-called excluding features could be incorporated into the theoretical background. Apart from definitions, we provide readers with a theoretical investigation. This investigation addresses two natural questions. Firstly, under which conditions (in which underlying algebraic structures) the given three natural approaches to the incorporation of excluding symptoms coincide. And secondly, under which conditions, the proposed incorporation of excluding features preserves the same natural and desirable properties similar to those preserved by fuzzy relational compositions. The positive impact of the incorporation on reducing the suspicions provided by the basic ``circlet'' composition without losing the possibly correct suspicion is demonstrated on an example.