The paper deals with one of the central topics of any word-formation theory, the problem of the headedness of complex words. A brief outline of the most influential views of the topic is followed by the delimitation of the basic features of head. Arguments are given in favour of an affix-pased approach to headedness, based on an onomasiological theory of word-formation. It is maintained that the conceptually identified onomasiological base can function as an indicator of head of naming units. With reference to prefix+WF base structures, an argument is put forward in favour of headedness of prefixes. The theory proposed is tested against Bauer's criteria of headedness. Based on the analysis presented the author of the paper does not share L. Bauer's scepticism reflected in his proposal of beheading the word.