The syntactic structure of sentences exhibits a striking regularity: de-pendencies tend to not cross when drawn above the sentence. Here we investigate two competing hypotheses for the origins of non-crossing de-pendencies. The traditional hypothesis is that the low frequency of de-pendency crossings arises from an independent principle of syntax that reduces crossings practically to zero. An alternative to this view is the hypothesis that crossings are a side effect of dependency lengths. Accord-ing to this view, sentences with shorter dependency lengths should tend to have fewer crossings. We recast the traditional view as a null hypothesis where one of the variables, i.e. the number of crossings, is mean indepen-dent of the other, i.e. the sum of dependency lengths. The alternative view is then a positive correlation between these two variables. In spite of the rough estimation of dependency crossings that this sum provides, we are able to reject the traditional view in the majority of languages considered. The alternative hypothesis can lead to a more parsimonious theory of syntax. 1

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