This paper presents some findings of my research on the systematic variation of German idioms, with attention focused on converse transformations such as (jmdm.) eins/eine/einen aufs Dach geben literally "to give someone one on the roof", meaning 'to strike someone' or 'to punish someone' -eins/eine/einen aufs Dach bekommen (von jmdm.) literally "to get one on the roof from someone", meaning 'to be struck by someone' or 'to be punished by someone'. To be subjected to converse transformations an idiom must have two active valencies. These valencies are usually filled by the Agent and Patient, more seldom by the Agent and Addressee or Beneficiary. This semantico-syntactic condition is also a constructional phenomenon because it is governed by the argument structure of a given expression. Within every semantic field, a certain constructional pattern underlies the converse transformation. Cf. for the semantic fields (1) PHYSICAL COERCION, PHYSICAL VIOLENCE and (2)