First against a conventional total-correctness background of wp semantics, we define a small family of compositions for predicate-pair specifications based on simple logical conjunction and disjunction, discussing the formal properties and offering an intuitive operational interpretation of each. Three of these compositions we recognise as familiar; the fourth one, our concert, is new but lacks any apparent use. Then we re-interpret our compositions in the context of general correctness to very useful effect.I am indebted to the anonymous reviewer whose extensive comments on a previous effort of mine directed at a different publication venue were partly instrumental in inspiring me to write this paper. In particular, that reviewer drew my attention to several other authors' works now referenced here.