Combined connectives arise when combining logics and are also useful for analyzing the common properties of two connectives within a given logic. A non-deterministic semantics and a Hilbert calculus are proposed for the meet-combination of connectives (and other language constructors) of any matrix logic endowed with a Hilbert calculus. The logic enriched with such combined connectives is shown to be a conservative extension of the original logic. It is also proved that both soundness and completeness are preserved. Illustrations are provided for classical propositional logic. Joint work with Cristina Sernadas, Joao Rasga and Paulo Mateus.