We present several algorithms for assigning heads in phrase structure trees, based on different linguistic intuitions on the role of heads in natural language syntax. Starting point of our approach is the observation that a head-annotated treebank defines a unique lexicalized tree substitution grammar. This allows us to go back and forth between the two representations, and define objective functions for the unsupervised learning of head assignments in terms of features of the implicit lexicalized tree grammars. We evaluate algorithms based on the match with gold standard head-annotations, and the comparative parsing accuracy of the lexicalized grammars they give rise to. On the first task, we approach the accuracy of hand-designed heuristics for English and inter-annotation-standard agreement for German. On the second task, the implied lexicalized grammars score 4% points higher on parsing accuracy than lexicalized grammars derived by commonly used heuristics.