There has been recent interest in applying cognitively- or empirically-motivated bounds on recursion depth to limit the search space of grammar induction models (Ponvert et al., 2011; Noji and Johnson, 2016; Shain et al., 2016). This work extends this depth-bounding approach to probabilistic context-free grammar induction (DB-PCFG), which has a smaller parameter space than hierarchical sequence models, and therefore more fully exploits the space reductions of depth-bounding. Results for this model on grammar acquisition from transcribed child-directed speech and newswire text exceed or are competitive with those of other models when evaluated on parse accuracy. Moreover, grammars acquired from this model demonstrate a consistent use of category labels, something which has not been demonstrated by other acquisition models.