OVER-elements indicating that an activity is carried out excessively are realized in one of two ways in Germanic languages: (i) as verbal prefixes (e.g., Engl. over-eat), or (ii) as prepositions (e.g., Icelandic borða- [yfir sig] 'eat [over ANPH]'). Prefixal OVER-strategies may or may not require an anaphor (e.g., Germ. sich über-essen vs. Engl. over-eat). Three major types of 'excessivity marking' with OVER can thus be distinguished: (i) [V [OVER ANPH]], (ii) [OVER-V ANPH], and (iii) [OVER-V]. This squib provides a unifying syntactic and semantic analysis of these strategies that regards OVER-elements as three-place predicates which may surface either as prepositions or as verbal prefixes. Two alternative, though closely related, semantic analyses are considered: (i) OVER indicates that the 'extent' (the number of minimal component events) of an event e instantiating a predicate P exceeds the 'natural extent' of a generic event instantiating P, relative to some individual x; (ii) the 'effect' of an event e instantiating a predicate P exceeds the 'natural effect' of a generic event instantiating P, relative to some individual x. While the second analysis prima facie appears to be more general than the first, there seem to be cases that require reference to the 'extent', rather than the 'effect', of an event. The squib concludes with a few remarks on challenges for future research.