Connectives typically relate two content units. However, corpus analysis shows several variants of the general connective construction (i.e., 'S1 Cn S2'), in which one of either segment 1 (S1) or segment 2 (S2) is optional or missing. The aim of this paper is to shed some light on the description of some variants of the connective construction where the connective is not followed by any explicit S2 or S2 is optional. These constructions are complete utterances but they can be considered defective constructions, since one of the slots of the prototypical construction does not include any linguistic material. The analysis focuses on corpus examples including a refutation marker where S2 is implicit, a case that is especially productive and varied in Catalan and in Spanish. Three defective constructions are identified, namely, (i) truncated constructions, (ii) embedded uses of a connective and (ii) reactive constructions. The data show that these defective connective constructions differ as for syntax, prosody, semantics and pragmatics. In monologic contexts, when the second segment is missing in the syntactic and prosodic unit considered, the connective is syntactically and prosodically related to S1. The connective can be located at the right-periphery of S1 (truncated construction) or at S1 middle field (embedded use of a connective). In dialogic contexts, the connective can act as a response to a previous turn and S2 can be either present or absent (reactive constructions). The different configurations match different intonation contours and pause patterns. In all cases, the connective weakens its connective function and adds a modal load, related to (inter)subjectification and intensification. This can be represented as a cline from discourse marking to modal marking.