A morphemic-indicational description of English but (and French mais) is proposed, showing that the uses of but whose closer equivalents (and French translation) are almost, except, only, and without, together with the considerable variety of its connective uses, may be accounted for within a single semantic description. It is shown that but and mais do not encode metacommunicational indications about the relationship between the connected utterances, as is commonly believed and asserted, but provide a rather aspectual information/indication, whose interpretation is contextual and constructional. It is hence shown that but and mais's description should be split into levels: the description of the indication encoded by the morpheme, which is active in all its uses, and the description of the constructional interpretation the indication receives when the morpheme is inserted in a given construction - such as But for X, Y or P but Q- or used in a specific context. The efficiency of this description is shown to support the Indicational-Indexical Semantics - IIS - framework approach. An introduction to this framework and to its relationship with the instructional semantics mainstream on the one hand, and with the procedural/conceptual distinction on the other hand, is also proposed.