Corpus data are used to investigate Yngve's claim that English usage avoids grammatical structures in which the number of left branches between any word and the root node of a sentence exceeds some fixed limit. The data do display a marked bias against left-branching, but the pattern of word-depths does not conform to Yngve's concept of a sharp limit. The bias could alternatively reflect a statistical invariance in the incidence of left-branching, but whether this is so depends on how left-branching is counted. Six nonequivalent measures are proposed; it turns out that one (and only one) of these yields strikingly constant figures for left-branching in real-life sentences over a wide range of lengths. This is not the measure suggested by Yngve's formulation; it is the measure whose invariance is arguably the most favourable for computational tractability.