This paper studies the properties of eight semantic consequence relations defined from a Tarski-logic **L** and a preference relation &\#8826;. They are equivalent to Shohams so-called preferential entailment for smooth model structures, but avoid certain problems of the latter in non-smooth configurations. Each of the logics can be characterized in terms of what we call multi-selection semantics. After discussing this type of semantics, we focus on some concrete proposals from the literature, checking a number of meta-theoretic properties and elaborating on their intuitive motivation. As it turns out, many of their meta-properties only hold in case &\#8826; is transitive. To tackle this problem, we propose slight modifications of each of the systems, showing the resulting logics to behave better at the intuitive level and in metatheoretic terms, for arbitrary &\#8826;.